Question

If `A = <4 ,2 ,5 >`, `B = <-8 ,3 ,6 >` and `C=A-B`, what is the angle between A and C?

Answer 1

1.04 radians

Explanation:

The angle between 2 vectors`ulacolor(black)(" and ") ulb` can be found using :

`costheta =( ula . ulb)/(|ula| |ulb|)`

where `thetacolor(black)(" is the angle between the vectors ")`

here C = A - B = (4,2,5) - (-8,3,6) = (12,-1,-1)

`ula . ulc = (4,2,5) . (12,-1,-1 ) = 48 - 2 - 5 = 41`

`|ula| = sqrt(4^2+2^2+5^2) = sqrt45`

and `|ulc| = sqrt(12^2+(-1)^2+(-1)^2) = sqrt146`

`rArr costheta = 41/(sqrt45 xx sqrt146`

and `theta = cos^-1 (41/(sqrt45 .sqrt146)) = 1.04color(black)(" radians ")`