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Let the line (x-2)/(3)=(y-1)/(-5)=(z+2)/...

Let the line `(x-2)/(3)=(y-1)/(-5)=(z+2)/(2)` lies in the plane `x+3y-alphaz+beta=0`. Then, `(alpha, beta)` equals

A

`(6,-17)`

B

`(-6,7)`

C

`(5,-15)`

D

`(-5,5)`

Text Solution

Verified by Experts

The correct Answer is:
B
Given line passes through `(2,1,-2)` and is parallel to `vecb=3hati-5hatj+2hatk`. A vector normal to the given plane is `vecn=hati+3hatj-alphahatk`.
If the line lies in the plane then (2,1,-2) lies on the plane and `vecb` is normal to `vecn`.
`:.2+3+2alpha+beta=0` and `3-15-2alpha=0`
`implies5+2alpha+beta=0` an `alpha=-6impliesalpha=-6` and `beta=7`
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