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If the angle theta between the line (x+1...

If the angle `theta` between the line `(x+1)/1=(y-1)/2=(z-2)/2` and the plane `2x-y+sqrt(lamdaz)+4=0` is such that `sin theta=1/3`, the value of `lamda` is

A

`-(4)/(3)`

B

`(3)/(4)`

C

`(-3)/(5)`

D

`(5)/(3)`

Text Solution

Verified by Experts

The correct Answer is:
D
Here, DR's of line
`a_(1)=1,b_(1)=2,c_(1)=2 `and the plane are `a_(2)=2,b_(2)=-1andc_(2)=sqrt(lamda)`.
`becausesintheta|{:(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))):}|`
`rArr" "(1)/(3)=|{:(2-2+2sqrt(lamda))/(sqrt(1+4+4)sqrt(4+1+lamda)):}|`
`rArrsqrt(5+lamda)=2sqrt(lamda)`
`rArr" "lamda=(5)/(3)`
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