PHYSICS MIDTERM EXAM

What is the angle between two vectors <8, -12, 8> and <7, 7, 7>?

Group of answer choices

62

72

82

52

82

Vectors include both magnitude and direction.

Vectors include both magnitude and direction.

True

False

True

Which of the following is true about an object moving in uniform accelerated motion?

Which of the following is true about an object moving in uniform accelerated motion?

The object is moving with constant velocity.

Its velocity vs. time graph is horizontal.

Its position vs. time graph is exponential.

The object is moving with zero acceleration.

Its position vs. time graph is exponential.

Which of the following is NOT TRUE about the two vectors illustrated in the figure above?

Group of answer choices

The vectors are parallel to each other.

The vectors are coinciding each other.

The vectors are of equal magnitudes.

The vectors are located in the first quadrant.

The vectors are coinciding each other.

A car traveling at 20 m/s rounds a curve so that its centripetal acceleration is 5 m/s2. What is the radius of the curve?

Group of answer choices

80 m

40 m

8 m

640 m

80 m

A golf ball is hit at an angle of 45° above the horizontal. What is the acceleration in m/s2 of the golf ball at the highest point in its trajectory? Neglect the effect of friction.

Group of answer choices

9.8 downwards

9.8 to the left

0

9.8 upwards

9.8 downwards

A ball is thrown horizontally from the top of a building 0.10 km high. The ball strikes the ground at a point 65 m horizontally away from and below the point of release. What is the speed in m/s of the ball just before it strikes the ground?

Group of answer choices

46 m/s

57 m/s

14 m/s

32 m/s

46 m/s

Which of the following is the unit vector representation of the vector <3,-2,-5>?

Group of answer choices

<-0.49, -0.32, -0.81>

<-0.49, 0.32, 0.81>

<0.49, 0.32, 0.81>

<0.49, -0.32, -0.81>

<0.49, -0.32, -0.81>

A projectile is directed toward the sky with an angle from the level ground. It reaches a range of 10 m in 10s. How long will it reach its maximum height above the ground?

Group of answer choices

5s

20s

15s

10s

10s

A projectile is fired from a gun and has initial horizontal and vertical components of velocity equal to 30 m/s and 40 m/s, respectively. Determine the magnitude of the initial velocity of the projectile.

Group of answer choices

70 m/s

60 m/s

50 m/s

80 m/s

50 m/s

A race car moving with a constant speed of 60 m/s completes one lap around a circular track in 50 s. What is the magnitude of the acceleration of the race car in m/s2?

Group of answer choices

7.5 m/s2

4.5 m/s2

5.5 m/s2

6.5 m/s2

7.5 m/s2

Gravity makes things fall on earth and has a constant rate of 9.8 m/s2

Group of answer choices

False

True

True

Volume is a vector quantity.

Group of answer choices

True

False

False

Given the vectors M = 2i - 3j and N = -3i + 2k, what is the resultant?

Group of answer choices

-i - k

i + 3j - 2k

-i - j

-i - 3j + 2k

-i - 3j + 2k

Given the statements below, which is/are ALWAYS true?

A. The cross product of 2 parallel vectors is always negative.

B. The dot product of perpendicular vectors is always maximum .

C. The vector sum of 2 opposite vectors is always zero.

Group of answer choices

Statements A and B only

Statements A, B, and C

Statement C onlyx

None of the statements

From his house, Brimstone walked 200m, 300 N of E. Then he walked an additional 300m towards West, to reach his destination. What is his displacement from his house to the destination?

Group of answer choices

-300i + 200j

173i +127j

-173i + 100j

-127i + 100j

-127i + 100j

What is the dot product of two vectors that are equal in magnitude and with 450 angle in between?

Group of answer choices

1.41

0.71

2

Cannot be determined with the given

Cannot be determined with the given

Vector A and Vector B has magnitudes of 15 and 10, respectively. If the angle between these vectors is 350, what is the magnitude of the cross product of vectors A and B?

Group of answer choices

86

105

123

0

86

The unit of centripetal acceleration is _____________.

Group of answer choices

m/s

Hertz

rpm

m/s2

m/s2

The only force that affects the motion of a projectile is

Group of answer choices

Gravity

Friction

Tension

Air Resistance

Gravity

Which of the following vectors is a unit vector?

Group of answer choices

<1,0,1>

<1,1,1>

<-1,0,0>

<-1,-1,-1>

<-1,0,0>

A projectile is fired at an angle of 45° above the horizontal. Assume that air resistance is not significant. While the projectile is in flight, its horizontal speed remains constant.

Group of answer choices

True

False

True

The magnitude of the first vector is twice that of the second vector. What is the cross product of these two vectors if they are directed opposite to each other?

Group of answer choices

2

Cannot be determined with the given

1

0

0

Given the vectors below. What is the angle between vectors C and D?

C = -3i - 3j

D = -5i - 5j

Group of answer choices

90

0

45

180

0

Which of the following is used to determine the direction of a cross-product result?

Group of answer choices

Head to Tail Method

Right Hand Rule

Pythagorean Theorem

Rule of Thumb

Right Hand Rule

Find the equilibrant of the 2 vectors given below.

P = <-2,10,-5>

Q = <3,2,1>

Group of answer choices

<6,20,-5>

<-6,-20,5>

<-1,-12,4>

<1,12,- 4>

<-1,-12,4>

Which of the following will result to a quantity with no direction?

Group of answer choices

cross product of 2 vectors

resultant of 2 vectors

equilibrant of 2 vectors

dot product of 2 vectors

dot product of 2 vectors

In which direction does the vector A = 3i - 2j point at?

Group of answer choices

68.20o N of E

33.69o S of E

68.20o S of E

27.20o N of E

33.69o S of E

Where 'a' is the length of the vector and 'B' is the angle it makes with the x-axis, what is the length of its component along the x-axis?

Group of answer choices

Bcosa

asinB

acosB

acosB

On what quadrant is the vector 3i - 15j located?

Group of answer choices

III

II

I

IV

IV

In which direction does the vector A = 2i - 5j point at?

Group of answer choices

68.20o N of E

27.20o S of E

27.20o N of E

68.20o S of E

68.20o S of E

Find the unit vector in the direction of <12,11>.

Group of answer choices

<12/16.28 , 11/16.28>

<16.28/11 , 16.28/12>

<16.28/12 , 16.28/11>

<11/16.28 , 12/16.28>

<12/16.28 , 11/16.28>

Which of the following vectors has a magnitude of 1?

Group of answer choices

<1,1,1>

<0,1,0>

<0,0,0>

<1,0,1>

<0,1,0>

Which of the following vectors has a magnitude of 3.32?

Group of answer choices

<1,3,2>

<1,2,3>

<3,2,2>

<3,1,1>

<3,1,1>

Displacement is a vector quantity.

Group of answer choices

True

False

True

Which of the following vector most likely points at an angle of inclination of 450?

Group of answer choices

<1,2>

<2,2>

<0,0>

<2,1>

<2,2>

Which of the following vector most likely points at an angle of inclination of 450?

Group of answer choices

A vector pointing towards the south-west direction.

A vector pointing towards the north-east direction.

A vector pointing towards the north-west direction.

A vector pointing towards the south-east direction.

A vector pointing towards the north-east direction.

Work is a vector quantity.

Group of answer choices

True

False

False

What is the magnitude of the vector <11, 0, 0>?

Group of answer choices

7

11

12

36

11

Where 'x' is the length of the vector and 'Y' is the angle it makes with the x-axis, what is the length of its component along the x-axis?

Group of answer choices

xcosY

xsinY

Ycosx

Ysinx

xcosY

Which of the following is true about vectors?

Group of answer choices

A vector is time-dependent.

A vector can be represented by matrices.

A vector has both curvature and magnitude.

Vectors can only be added, not subtracted.

A vector can be represented by matrices.

On what quadrant is the vector -3j + 15i located?

Group of answer choices

III

II

I

IV

I

Resistance is a vector quantity.

Group of answer choices

False

True

False

The vector <0,1,0> is a unit vector.

Group of answer choices

False

True

True

What is the unit vector representation of the vector <-2,3>?

Group of answer choices

<-2/sqrt(13), 3/sqrt(13)>

<2/13, 3/13>

<-2/13, 3/13>

<2/sqrt(13), 3/sqrt(13)>

<-2/sqrt(13), 3/sqrt(13)>

Suppose that A = 3i − j + 2k. What is the magnitude of the vector A?

Group of answer choices

sqrt(14)

14

4

sqrt(4)

sqrt(14)

Suppose that A = 10i + j - 4k. What is the magnitude of the vector A?

Group of answer choices

sqrt(117)

15

sqrt(15)

17

sqrt(117)

How many components does a vector in 1D space have?

Group of answer choices

3

1

4

2

1

All vectors have unit vector representations.

Group of answer choices

False

True

True

Which of the following vectors is in 3D-space?

Group of answer choices

<0,1,1>

<1,1,1>

<1,1,0>

<0,0,1>

<1,1,1>

Find the resultant vector of the vectors given below.

A = <12,10,-8>

B = <-8,10,12>

Group of answer choices

<10,10,10>

<4,20,4>

<10,20,10>

<4,0,4>

<4,20,4>

Find the resultant vector of the vectors given below.

A = <-12,-10,-8>

B = <8,10,12>

Group of answer choices

<10,20,10>

<4,0,4>

<10,10,10>

<-4,0,4>

<-4,0,4>

What must be the x-component of a unit vector if it is along the y-axis?

Group of answer choices

1

2

0

-1

0

The vector <1,1,0> is a unit vector.

Group of answer choices

False

True

False

Suppose that B = -3i + j - 2k. What is the magnitude of the vector A?

Group of answer choices

14

sqrt(4)

sqrt(14)

4

sqrt(14)

Suppose that B = -2i + j - 6k. What is the magnitude of the vector A?

Group of answer choices

3

sqrt(14)

8

sqrt(41)

sqrt(41)

What is the magnitude of the vector <0, 0, 6>?

Group of answer choices

5

6

7

36

6

A vector is always __________ to its unit vector representation.

Group of answer choices

intersecting

coinciding

orthogonal

perpendicular

coinciding

Temperature is a vector quantity.

Group of answer choices

False

True

False

Which of the following quantities is scalar?

Group of answer choices

density

torque

centrifugal force

centripetal force

density

On what plane is the vector <0,1,1> located?

Group of answer choices

xy plane

yz plane

along the x-axis

xz plane

yz plane

Mass is considered as a scalar quantity. The SI base unit of mass is ________.

Group of answer choices

gram

pound

kilogram

ounce

kilogram

Torque is a vector quantity.

Group of answer choices

False

True

True

What is the magnitude of the vector 4i - 8j - 12k?

Group of answer choices

12.22

14.97

17.36

15.29

14.97

On what axis is the unit vector <0,1,0> along?

Group of answer choices

origin

z-axis

x-axis

y-axis

y-axis

Which of the following vectors is in 3D space?

Group of answer choices

<0,0,1>

<0,1,0>

<1,0,1>

<1,1,1>

<1,1,1>

Where 'x' is the length of the vector and 'Y' is the angle it makes with the x-axis, what is the length of its component along the y-axis?

Group of answer choices

Ysinx

xcosY

Ycosx

xsinY

xsinY

Energy is a vector quantity.

Group of answer choices

True

False

False

On what plane is the vector <1,0,1> located?

Group of answer choices

yz plane

xz plane

xy plane

along the x-axis

xz plane

On what axis is the unit vector <0,0,1> along?

Group of answer choices

origin

x-axis

y-axis

z-axis

z-axis

What is the magnitude of the vector 2i + 4j + 2k?

Group of answer choices

1.2

3.3

5.6

4.9

4.9

On what plane is the vector <1,0,0> located?

Group of answer choices

xy plane

along the x-axis

xz plane

yz plane

along the x-axis

How many components does a vector in 2D space have?

Group of answer choices

3

1

2

4

2

What is the unit vector representation of the vector <4,5>?

Group of answer choices

<4/sqrt(41), 5/sqrt(41)>

<5/sqrt(41), 4/sqrt(41)>

<4/41, 5/41>

<5/41, 4/41>

<4/sqrt(41), 5/sqrt(41)>

To get the unit vector in the direction of a given vector, the components of the vector must be divided to its magnitude.

Group of answer choices

False

True

True

The vector <1,0,1,5,6,0,1> is a vector with how many components?

Group of answer choices

6

5

4

7

5

Find the equilibrant vector of the vectors given below.

A = <-3,0,6>

B = <8,12,1>

Group of answer choices

<5,12,5>

<12,5,7>

<-5,-12,-7>

<7,5,12>

<-5,-12,-7>

Find the equilibrant vector of the vectors given below.

A = <-12,-10,-8>

B = <8,10,12>

Group of answer choices

<4,0,-4>

<4,0,4>

<10,20,10>

<10,10,10>

<4,0,-4>

Find the equilibrant vector of the vectors given below.

A = <12,10,8>

B = <8,10,12>

<-20,-20,-20>

Find the equilibrant vector of the vectors given below.

A = <12,10,-8>

B = <-8,10,12>

Group of answer choices

<-4,-20,-4>

<10,10,10>

<4,0,4>

<10,20,10>

<-4,-20,-4>

The dot product of <12,0,-12> and <-6,8,-7> is ___________.

Group of answer choices

12

28

-12

-28

12

What is the angle between two vectors <1,6,9> and <2,-2,5>?

Group of answer choices

34

42

56

65

56

Given the vectors below. What is the magnitude of the cross product of A and C?

A = 2i + 2j - 2k

B = i + 2k

C = 3i - 12j + 6k

Group of answer choices

11.86

43.22

9.73

36.99

36.99

Given the vectors below. What is the dot product of vectors A and B?

A = 2i + 2j - 2k

B = i + 2k

C = 3i - 12j +6k

Group of answer choices

0

2

-2

-4

-2

Cosmo and Wanda wanted to get a dot product result of minimum. What must be the angle between two vectors that they should get?

Group of answer choices

900

2700

1800

4500

180

Which of the following is true about the properties of dot product?

Group of answer choices

The dot product operation is commutative.

The dot product of two vectors that are orthogonal is always positive.

The dot product operation is anti-commutative.

The dot product of two vectors that are anti-parallel is always zero.

The dot product operation is commutative.

Find the equilibrant vector of the vectors given below.

A = <5,10,15>

B = <5,5,5>

Group of answer choices

<10,15,10>

<20,15,10>

<-10,-15,-20>

<20,15,20>

<-10,-15,-20>

Find the equilibrant vector of the vectors given below.

A = <0,0,-8>

B = <8,0,0>

Group of answer choices

<8,0,8>

<-8,0,8>

<8,0,-8>

<-8,0,-8>

<-8,0,8>

Given the vectors below. What is the dot product of vectors B and C?

A = 2i + 2j - 2k

B = i + 2k

C = 3i - 12j + 6k

Group of answer choices

-15

-6

15

6

15

The dot product of <-3,5,0> and <0,20,8> is ___________.

Group of answer choices

400

300

100

200

100

The dot product of <2,-4,6> and <1,1,0> is ___________.

Group of answer choices

2

-2

4

-4

-2

Given the vectors below. What is the angle between the vectors A and C?

A = 7i + 5j

B = 3i + 3k

C = -i - j + 4k

Group of answer choices

119.05

72.38

132.96

109.20

109.20

The dot product of <11,0,0> and <0,11,11> is ___________.

Group of answer choices

0

121

11

-11

0

Which of the following quantities is not involved when solving for the dot product of two vectors A and B?

Group of answer choices

The angle of inclination of A

The angle between A and B

The magnitude of B

The magnitude of A

The angle of inclination of A

What is the cross product of <2,-2,2> and <-1,-1,-1>?

Group of answer choices

<0, 4, 4>

<-4, 0, 4>

<4, 4, -4>

<4, 0, -4>

<4, 0, -4>

What is the cross product of <2,-2,2> and <-1,1,1>?

Group of answer choices

<0, 2, 2>

<-4, -4, 0>

<0, -5, 5>

<0, 3, -3>

<-4, -4, 0>

The cross product of two vectors that are anti-parallel is ________.

Group of answer choices

zero

minimum

maximum

negative

zero

What is the equilibrant vector if you add all the vectors A, B, and C?

A = 2i - 3j + 3k

B = 4j + 2i - 5k

C = 5i - 2j + 5k

Group of answer choices

-11i + 3j - 3k

9i - j + 3k

-9i + j - 3k

11i + 3j + 3k

-9i + j - 3k

Which of the following angles between two vectors will give you a dot product of zero?

Group of answer choices

270

360

0

180

270

The vector <1,0,-3,-7,5,6,0,1> is a vector with how many components?

Group of answer choices

4

7

5

6

6