The angle between the line `(3x-1)/3=(y+3)/(-1)=(5-2z)/4` and the plane `3x-3y-6z=10` is equal to

Options

A. `(pi)/(6)`
B. `(pi)/(4)`
C. `(pi)/(3)`
D. `(pi)/(2)`

Answer

D

Explanation

Given line and plane can be rewritten as
` ( 3x - 1 ) /( 3 ) = ( y + 3 ) /( - 1 ) = ( 5 - 2z ) /( 4 ) `
` ( x - ( 1 ) /( 3 )) /( 1 ) = ( y + 3 ) /( - 1 ) = (( z - ( 5 ) /( 2 ))) /( - 2 ) `
and ` x - y - 2z = 0 `
Here, ` a _ 1 = 1, b _ 1 = - 1, c _ 1 = - 2 `
and ` a _ 2 = 1, b _ 2 = - 1, c _ 2 = - 2 `
` therefore sin theta = ( a _ 1 a_ 2 + b _ 1b _ 2 + c _ 1 c _ 2 ) /( sqrt( a _ 1 ^ 2 + b _ 1 ^ 2 + c _ 1 ^ 2 ) sqrt( a _ 2 ^ 2 + b _ 2 ^ 2 + c _ 2 ^2)) `
` = ( 6 ) /( sqrt6 sqrt 6 ) = 1 rArr theta = ( pi ) /( 2 ) `