Find the angle between the planes ` vec rdot(2 hat i- hat j+ hat k)=6a n d vec rdot( hat i+ hat j+2 hat k)=5.`

Options

A. `(pi)/(2)`
B. `(pi)/(4)`
C. `pi`
D. `(pi)/(3)`

Answer

D

Explanation

Here, `n_(1)=2hat(i)-hat(j)+hat(k)andn_(2)=hat(i)+2hat(k)` we know that `costheta=(n_(1)*n_(2))/(|n_(1)||n_(2)|)`
`costheta=((2hat(i)-hat(j)+hat(k))*(hat(i)+hat(j)+2hat(k)))/(|2hat(i)-hat(j)+hat(k)||hat(i)=hat(j)+2hat(k)|)`
`=(2-1+2)/(sqrt(4+1+1)sqrt(1+1+4))=(3)/(6)=(1)/(2)`
`rArrtheta=(pi)/(3)`