Angle between the line `r=(-hati+3hatj+3hatk)+t(2hati+3hatj+6hatk)` and the plane `r(-hati+hatj+hatk)` is

Options

A. `sin^(-1)((1)/(sqrt(3))`
B. `sin^(-1)((1)/(sqrt(2))`
C. `sin^(-1)((2)/(sqrt(3)))`
D. `sin^(-1)((3)/(sqrt(2)))`

Answer

A

Explanation

Angle between line and plane is given by
`sintheta=((2hati+3hatj+6hatk)*(-hati+hatj+hatk))/(sqrt(4+9+36)sqrt(1+1+1))`
`=(-2+3+6)/(7sqrt(3))=(1)/(sqrt(3))`
`impliestheta=sin^(-1)((1)/(sqrt(3)))`