Vector a is (4,4,4)T Vector b is (4,0,4)T Calculate: au · bu = cos θ
|a| =
(16 + 16 + 16) = 4
3 , |b| =
(16 + 16) = 4
2
au = (4, 4, 4)T/(4
3) , bu = (4, 0, 4)T/(4
2 )
au · bu = (16 + 16)/( (4
3)(4
2) )
= 2/(
3
2 ) =
2 /
3 = cos θ
cos θ = 0.81649, θ = 35.26°
The nasty math in the previous exercise is not the real purpose of all this.
The goal is to illustrate the formula
The figure shows two vectors, represented by:
Rotate the figure to get a better sense of the angle. What you would like to do is to lay a sheet of paper across the two vectors, trace them onto the paper, and then measure the angle with a protractor. But this is hard to do with a computer screen.