The angle between the line `(x-3)/(2)=(y-1)/(1)=(z+4)/(-2)` and the plane, `x+y+z+5=0` is

Options

A. `sin^(-1)((2)/(sqrt(3)))`
B. `sin^(-1)((1)/(sqrt(3)))`
C. `(pi)/(4)`
D. `sin^(-1)((1)/(3sqrt(3)))`

Answer

D

Explanation

`because` Direction ratios of lines and planes are `(a_1,b_1,c_1)=(2,1-2)` and `(a_2,b_2,c_2)=(1,1,1)`
`therefore sin theta=(a,a_2+b_1b_2+c_1c_2)/(sqrt(a_(1)^(2)+b_(1)^(2)+c_(1)^(2))sqrt(a_(2)^(2)+b_(2)^(2)+c_(2)^(2)))`
`=(2+1-2)/(sqrt(4+1+4)sqrt(1+1+1))`
`rArr theta=sin^(-1)((1)/(3sqrt(3)))`