Question

What is the angle between `<4 , 7 , -4 >` and `< 5 , 2 , 3 >`?

Answer 1

`theta=66.64^0`

Explanation:

Let `vecu =<4,7, -4> and vecv =<5,2,3> ; theta` be the angle between them ; then we know `cos theta= (vecu*vecv)/(||vecu||*||vecv||)=((4.5)+(7*2)+(-4*3))/(sqrt(4^2+7^2+(-4)^2)* (sqrt(5^2+2^2+3^2))` `= 22/(sqrt81*sqrt38)=22/(9*sqrt38)=0.3965:. theta=cos^-1(0.3965)=66.64^0`[Ans]