Math Review

dot product equation

|a||b|cos(angle btw)

cross product 2D equation

|a||b|sin(angle btw)

cross product 3D

use table - make sure j is negative

adding vectors

add each component

projection of vector a on b

|a||b|/|b||b| (vector b)

collinear definition

points that lie on the same line

plane equation with P(x0,y0,z0) and vector <a,b,c>

a(x-x0)+b(y-y0)+c(z-z0) = 0

plane equation format

Ax + By + Cz +D = 0

circle equation format

x²+y²+z²=r²

distance formula

sqrt((x2-x1)²+(y2-y1)²+(z2-z1)²)

what does the cross product give you

1. the vector perpendicular to both

2. magnitude gives area of a parallelogram

scalar projection equation

dot product of a and b / |b|

symmetric form of a line format

x-x0/a = y-y0/b = z-z0/c

if the n vectors of two planes are parallel what does that say about the planes

the planes are parallel

angle between two planes

dot product of their n vectors and solve for theta

if dot product is 0

vectors are perpendicular