Vector Formulas/Properties

u ⋅ u = ?

|u|²

T/F: u ⋅ v = v ⋅ u

t

u ⋅ (v ⋅ w) =

u ⋅ v + u ⋅ w

(au) ⋅ v =

a(u ⋅ v)

0 ⋅ u = 

0

Angle Between Vectors Using Dot Product

u ⋅ v = |u||v|cos(θ)

proj_vu =

v(u ⋅ v)/|v| 

(ru) x (sv) =

rs(u x v)

u x (v + w)

u x v + u x w

0 x u =

0

u x u

0

T/F: u ⋅ (v × w) = v ⋅ (w × u) = w ⋅ (u × v)

T

T/F: u x v = v x u

F

Area of a Parallelogram formed by 2 vectors

|u x v|

Volume of a parallelpiped formed by 3 vectors

(u x v) ⋅ w

Area of a triangle using 3 points (P, Q, R)

|PQ x PR| / 2

Distance from a point to a line

d = |PS x v| / |v|

Distance from a point to a plane

d = |PS ⋅ n/|n||