Question

What is the angle between `< 6 , 1 , -4 >` and `< 2 , -3 , 2 >`?

Answer 1

`88^@`

Explanation:

To find the angle between 2 vectors use the following formula :

`costheta =( veca.vecb)/((|veca| xx |vecb|)`

where a and b represent the 2 vectors and
`theta color(black)(" the angle between them")`

let `veca = (6,1,-4) , vecb = (2 , - 3 , 2 )`

then `veca . vecb = 12 - 3 - 8 = 1`

and `|veca| = sqrt(6^2+1^2+(-4)^2) =sqrt(36+1+16) =sqrt53`

`|vecb| = sqrt(2^2+(-3)^2+2^2) = sqrt(4+9+4) = sqrt17`

hence `costheta = 1/(sqrt53 xx sqrt17)`

`theta = cos^-1 (1/(sqrt901)) = 88^@`