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The angle between r=(1+2mu)hat(i)+(2+m...

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

A

`sin^(-1)((15)/(21))`

B

`cos^(-1)((16)/(21))`

C

`sin^(-1)((16)/(21))`

D

`(pi)/(2)`

Text Solution

Verified by Experts

The correct Answer is:
C
The given 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))`
Vector equation of a line written in cartesian form is
`(x-1)/(2)=(y-2)/(1)=(z+1)/(2)`
`:.` Angle between a line and a plane is given by
`sintheta=(a_(1)a_(2)+b_(1)b_(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)))`
`=(2xx3+1xx(-2)+2xx6)/(sqrt(4+1+4)sqrt(9+4+36))=(16)/(21)`
`rArr" "theta=sin^(-1)((16)/(21))`
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