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Let P(3,2,6) be a point in space and Q b...

Let `P(3,2,6)` be a point in space and `Q` be a point on line ` vec r=( hat i- hat j+2 hat k)+mu(-3 hat i+ hat j+5 hat k)dot` Then the value of `mu` for which the vector ` vec P Q` is parallel to the plane `x-4y+3z=1` is a. 1/4 b. -1/4 c. 1/8 d. -1/8

A

`1/4`

B

`-1/4`

C

`1/8`

D

`-1/8`

Text Solution

Verified by Experts

The correct Answer is:
A
Let the position vector of `Q` be
`(hati-hatj+2hatk)+mu(-3hati+hatj+5hatk)`
`=(-3mu+1)hati+(mu-1)hatj+(5mu2)hatk`.
Then `vec(PQ)=(-3mu-2)hati+(mu-3)hatj+(5mu-4)hatk`
It is given that `vec(PQ)` is parallel to the plane `x-4y+3z=1` whose normal is `vecn=hati-4hatj+3hatk`.
`:.vec(PQ).vecn(n)=0`
`implies(-3mu-2)=4(mu-3)+3(5mu-4)=0impliesmu=1/4`
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