math ch16: vectors

can be described by a single number called scalar

physical quantities indicate the

a quantity that has magnitude and direction

time, distance,, mass, speed, energy, area. temperature, and pressure are all examples of

force, displacement, gravity, velocity, momentum, acceleration, and angular velocity are all examples of

in a line AB, A is called a

in a line AB, B is called the

the vector AB is denoted in three ways:

the directed angle between the vector and the positive x axis is the

the direction of the vector can also be given as

a directional measurement between 0 and 90 east or west of the north-south line

a directional measurement where the angle is measured clockwise from north

have the same or opposite direction but not necessarily the same magnitude

have the same magnitude and direction

have the same magnitude but opposite direction

the sum of two or more vectors

finding resultants is by two ways

the triangle method uses

the parallelogram method uses

two or more vectors with a sum that is a vector r are called

while components can have any direction, it is often useful to express or resolve a vector into

the rectangular components are

I x i=

I y I=

the component form of a vector with initial point A and terminal point B is given by

magnitude of a vector is given by

magnitude of a vector represented by (x,y) is given by

for a (a1,a2) and b(b1,b2), adding a +b =

subtraction of a-b=

scalar multiplication ka=

a vector that has a magnitude of one unit

u=

the unit vectors in the direction of the positive x and y axis are denoted by

vectors i and j are called

we can write the vector (a,b) in the form of ai+bj as

the vector v can be written in component form or as a linear combination of i and j using the

v=(a,b) when expressed in sin and cos is

the direction angle x of vector v can be found using the trignometric equations:

for a given vector v, if x=tan^-1b/a, a is

for a given vector, if x=tan^-1b/a + pi, a is

dot product of a and b vectors is defined as

orthagonal vectors are

a and b vectors are only orthagonal if a.b=

if x is the angle between nonzero vectors a and b, then cosx=

an axis that passes through the origin and is perpendicular to the x and y axis in a three dimensional coordinate plane is called

if a(a1,a2) and b(b1,2) and z(z1,z2), then AB vector =

the distance between a(x1,y1.z1) and b(x2,y2,z2) is

magnitude of a vector (xyz) is given as

the midpoint of AB in a three dimensional plane is

unit vectors are:

i=

j=

k=

the linear combination of v=(v1,v2,v3)=

the magnitude of the vector v=(v1,v2,v3) is

the unit vector u in the direction of v is u=

if a=a1i + a2j +a3k and b=b1i+b2j+b3k, the corss product of a and b is the vector:

a x b=

if a x b =c, c is

if a and b are adjacent sides in a parallelogram, then I a x b I equals the

three vectors that lie in different planes but share the sam einitial point determine the adjacent angles of a

the absolute value of the triple scalar product of these two vectors represents the