The angle between `r=(1+2mu)hat(i)+(2+mu)hat(j)+(2mu-1)hat(k)` and the plane `3x-2y+6x=0` (where, `mu` is a scalar) is

Options

A. `sin^(-1)((15)/(21))`
B. `cos^(-1)((16)/(21))`
C. `sin^(-1)((16)/(21))`
D. `(pi)/(2)`

Answer

C

Explanation

The givan line is `r=(1+2mu)hat(i)(2+mu)hat(j)+(2mu-1)hat(k)`
`=(hat(i)+2hat(j)-hat(k))+mu(2hat(i)+hat(j)+2hat(k))`
The cartesian form of a line is `(x-1)/(2)=(y-2)/(1)=(z+1)/(2)`
Also, given `3x-2y+6z=0`
`:.` Angle between the line and the plane is
`sintheta=(2xx3+1xx(-2)+2xx6)/(sqrt(4+1+4)sqrt(9+4+36))=(6-2+12)/(21)=(16)/(21)`
`rArr" "theta=sin^(-1)((16)/(21))`