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Let A be a point on the line vecr = (1- ...

Let A be a point on the line `vecr = (1- 5 mu) hati + (3mu - 1) hatj + (5 + 7mu )hatk` and B (8, 2, 6) be a point in the space. Then the value of `mu` for which the vector `vec(AB)` is parallel to the plane x - 4y + 3z = 1 is:

A

`1/4`

B

`- 5/4`

C

`- 1/2`

D

`- 3/4`

Text Solution

Verified by Experts

The correct Answer is:
C
`vec(AB) = (5mu + 7) hati + ( 3 - 3 mu )hatj + (1 - 7mu) hatk`
Parallel to ` x - 4 y +3z = 1`
`(5mu + 7) - 4( 3 - 3mu) + 3 (1 - 7mu) = 1 = 0`
` 7 + 5mu - 12 + 12mu + 3 - 21mu = 1 = 0`
` -4 mu = 2 , " " mu = - 1/2`
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