The angle between `hati` and line of the intersection of the plane `vecr.(hati+2hatj+3hatk)=0andvecr.(3hati+3hatj+hatk)=0` is

Options

A. `cos^(-1)((1)/(3))`
B. `cos^(-1)((1)/(sqrt3))`
C. `cos^(-1)((2)/(sqrt3))`
D. none of these

Answer

d

Explanation

Line of intersection of `vecr.(hati+2hatj+3hatk)=0andvecr.(3hati+3hatj+hatk)=0` will be parellel to `(hati+hatj+hatk)xx(hati+2hatj+3hatk),i.e.,7hati-8hatj+3hatk.`
If the required angle is `theta`, then
`costheta=(7)/(sqrt(49+64+9))=(7)/(sqrt122)`