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If the lines (x-1)/(-3)=(y-2)/(2k)=(z-3...

If the lines `(x-1)/(-3)=(y-2)/(2k)=(z-3)/2`and `(x-1)/(3k)=(y-1)/1=(z-6)/(-5)`are perpendicular, find the value of k.

A

`(-10)/(7)`

B

`(10)/(7)`

C

`(-10)/(11)`

D

`(10)/(11)`

Text Solution

Verified by Experts

The correct Answer is:
A
Given lines can be rewritten as
`(x-1)/(-3)=(y-2)/(2alpha)=(z-3)/(2)`
and `(x-1)/(3alpha)=(y-1)/(1)=(z-6)/(-5)`
`therefore` The direction ratio of given lines are `(-3,2,alpha,2) and (3alpha,1,-5)`
Since, lines are perependicular
`therefore a_(1)a_(2)=b_(1)b_(2)+c_(1)c_(2)=0`
`Rightarrow (-3)(3alpha)+2alpha(1)+2(-5)=0`
`Rightarrow -9alpha+2alpha-10=0`
`Rightarrow alpha=-10/7`
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