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If angle theta bertween the line (x+1)/1...

If angle `theta` bertween the line `(x+1)/1=(y-1)/2=(z-2)/2` and the plane `2x-y+sqrt(lambda)z+4=0` is such that `sin theta=1//3,` the value of `lambda` is
a. `-3/5`
b. `5/3`
c. `-4/3`
d. `3/4`

A

`-4//3`

B

`3//4`

C

`-3//5`

D

`5//3`

Text Solution

Verified by Experts

The correct Answer is:
D
The given line is parallel to the vector `vecb=hati+2hatj+2hatk` and the given plane is normal to the vector `vecn=2hati-hatj+sqrt(lamda)hatk`.
`:.sin theta=(vecb.vecn)/(|vecb||vecn|)`
`implies1/3=(2-2+2sqrt(lamda))/(3xxsqrt(lamda+5))impliessqrt(lamda+5)=2sqrt(lamda)implieslamda=5/3`
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