The plane `2x-3y+6z-11=0` makes an angle `sin^(-1)(alpha)` with X-axis. The value of `alpha` is

Options

A. `(sqrt(3))/(2)`
B. `(sqrt(2))/(3)`
C. `(2)/(7)`
D. `(3)/(7)`

Answer

C

Explanation

Since, the plane `2x-3y+6z-11=0` makes an angle `sin^(-1)(alpha)` with X-axis Therefore the firection ratio of X-axis is (1.0.0)
`:." "sin(sin^(-1)alpha)=|{:(hat(i)*(2hat(i)-3hat(i)+6hat(k)))/(sqrt(1^(2))sqrt(2^(2)+(-3)^(2)+6^(2))):}|`
`rArr" "alpha=(2)/(1sqrt(49))rArralpha=(2)/(7)`