Question

Given the vectors
`vec(A)=2hat(i)+3hat(j)-hat(k)`
`vec(B)=3hat(i)-2hat(j)-2hat(k)`
& `" " vec(c)=phat(i)+phat(j)+2phat(k)`
Find the angle between `(vec(A)-vec(B))` & `vec(C)`

Answer 1

Correct Answer - `thetacos^(-1)((sqrt(2))/(3))`
`vec(A)-vec(B)=-hat(i)+5hat(j)+1hat(k)`
`vec(C)=Phat(i)+P5hat(j)+2Phat(k)`
`(vec(A)-vec(B)).vec(C)=|vec(A)-vec(B)||vec(c)| cos theta`
`cos theta=(6P)/(sqrt(27)sqrt(6P^(2)))=(sqrt2)/(3)`
`theta=cos^(-1)((sqrt(2))/(3))`