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

Options

A. `1//4`
B. `-1//4`
C. `1//8`
D. `-1//8`

Answer

a

Explanation

Any point on the line can be taken as
`" "Q= {(1-3mu), (mu-1), (5mu+2)}`
`" "vec(PQ)= {-3mu-2, mu-3, 5mu-4)
Now, 1(-3mu-2)-4(mu-3)+3(5mu-4)=0`
or `" "-3mu-2-4mu+12+15mu-12=0`
or `" "8mu= 2 or mu = 1//4`