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

Options

A. `cos^(-1)(5/14)`
B. `sin^(-1)(5/14)`
C. `cos^(-1)(3/7)`
D. `sin^(-1)(3/7)`

Answer

b

Explanation

D.r,s of the given line are `1,-2,-3`.
D.r.'s of the normal to the given plane are `2,-3,1`.
`therefore sintheta= |(1 xx 2)+(-2) x (-3) + (-3) xx 1|/(sqrt(^(2)+(-2)^(2)+(-3)^(2))(sqrt(2)^(2)+(-3)^(2)+1^(2))`
`=5/14 rArr theta= sin^(-1)(5/14)`.