11.2-vectors In space

R,emeber that a vector is a line with direction and magnitude. It is denoted by v=<v1,v2,v3>

To find the points of a vector we usually subtract the terminal point by the initial points

Here a few things regarding vectors in space

Let's say we had to give the component form, the length, and unit vector of v with initial point (3,4,2) and terminal point (3,6,4).

V= <3-3,6-4,4-2> = <0,2,2> 

||v|| = [2^2+2^2]^1/2 = 8^1/2

U = <0,2,2>/8^1/2 = <0,1/2^1/2, 1/2^1/2>

Angle between two vectors 

Cos theta = (u * v)/||u||||v||