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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
Given, `OQ=(1-3mu)hati+(mu-1)hatj+(5mu+2)hatk`
and `OP=3hati+2hatj+6hatk" "["where, O is origin"]`

Now, `PQ=(1-3mu-3)hati+(mu-1-2)hatj+(5mu+2-6)hatk`
`=(-2-3mu)hati+(mu-3)hatj+(5mu-4)hatk`
`because"PQ is parallel to the plane "x-4y+3z=1.`
`:.-2-3mu-4mu+12+15mu-12=0`
`implies" "8mu=2impliesmu=(1)/(4)`
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