cross/dot product

a x a

0

Vectors a and b are parallel if :

a×b = 0

Area of a parallelogram

a x b

(ca) x b

c(a x b) = a x (cb)
where c is scalar

a x (b + c)

a x b + a x c

Torque

T = r x F

scalar projection of b onto a

|b|cos(theta)

vector projection of b onto a

|a|cos(theta)(b/|b|)

two vectors a and b are orthogonal if

a . b = 0

a . b =

|a||b| cos θ=a1b1+a2b2

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

Work

W = F . D

a . a

|a|²

a . b = b . a

true

unit vector in direction of another vector

(1/|v|)

Standard Unit Vectors

i=

Linear combination of standard vectors

vector values times the standard unit vectors
ex:

Triangle Law

Line vectors A and B up head to tail and A+B is the vector that completes the triangle

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

Subtraction of vectors

Head of second to head of first, B-A has the same magnitude but opposite direction to A-B

if a.b=0

vectors are orthogonal

Relationship between angles and cosines of dot product

θ=0 if cosθ=1
0