Question

If `A = <6 ,1 ,5 >`, `B = <4 ,6 ,-1 >` and `C=A-B`, what is the angle between A and C?

Answer 1

0.95 radians

Explanation:

To find the angle between 2 vectors `ulacolor(black)(" and ") ulc`

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

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

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

now `ula . ulc = (6,1,5) . (2,-5,6) =12-5+30 = 37`

`|ula| = sqrt(6^2+1^2+5^2) = sqrt(36+1+25) = sqrt62`

and `|ulc| = sqrt(2^2+(-5)^2 +6^2) = sqrt(4 + 25 + 36) = sqrt65`

hence `costheta = 37/(sqrt62 xx sqrt65)`

`rArr theta = cos^-1(37/(sqrt62 xx sqrt65)) = 0.95color(black)(" radians ")`