cross/dot product

0.0(0)
learnLearn
examPractice Test
spaced repetitionSpaced Repetition
heart puzzleMatch
flashcardsFlashcards
Card Sorting

1/21

encourage image

There's no tags or description

Looks like no tags are added yet.

Study Analytics
Name
Mastery
Learn
Test
Matching
Spaced

No study sessions yet.

22 Terms

1
New cards
a x a
0
2
New cards
Vectors a and b are parallel if :
aĂ—b = 0
3
New cards
Area of a parallelogram
a x b
4
New cards
(ca) x b
c(a x b) = a x (cb)
where c is scalar
5
New cards
a x (b + c)
a x b + a x c
6
New cards
Torque
T = r x F
T = r x F
7
New cards
scalar projection of b onto a
|b|cos(theta)
|b|cos(theta)
8
New cards
vector projection of b onto a
|a|cos(theta)(b/|b|)
|a|cos(theta)(b/|b|)
9
New cards
two vectors a and b are orthogonal if
a . b = 0
10
New cards
a . b =
|a||b| cos θ=a1b1+a2b2
11
New cards
a x b =
|a| |b| sinθ(n) or created matrix with standard unit vectors, first components, second components and then solve
-always orthogonal to both vectors
-use right hand rule to find direction
12
New cards
Work
W = F . D
13
New cards
a . a
|a|²
14
New cards
a . b = b . a
true
15
New cards
unit vector in direction of another vector
(1/|v|)
16
New cards
Standard Unit Vectors
i=
17
New cards
Linear combination of standard vectors
vector values times the standard unit vectors
ex:
18
New cards
Triangle Law
Line vectors A and B up head to tail and A+B is the vector that completes the triangle
19
New cards
parallelogram law
Line vectors A and B up tail to tail and create a parallelogram
-A+B is the vector from the tails to the opposite side
-A-B or B-A is the vector that connects the heads
20
New cards
Subtraction of vectors
Head of second to head of first, B-A has the same magnitude but opposite direction to A-B
21
New cards
if a.b=0
vectors are orthogonal
22
New cards
Relationship between angles and cosines of dot product
θ=0 if cosθ=1
0