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If the lines (x-1)/2=(y+1)/3=(z-1)/4a n ...

If the lines `(x-1)/2=(y+1)/3=(z-1)/4a n d(x-3)/1=(y-k)/2=z/1` intersect, then find the value of `kdot`

A

`3/2`

B

`9/2`

C

`-2/9`

D

`-3/2`

Text Solution

Verified by Experts

The correct Answer is:
B
We know that the lies
`(x-x_(1))/(l_(1))=(y-y_(1))/(m_(1))=(z-z_(1))/(n_(1))` and `(x-x_(2))/(l_(2))=(y-y_(2))/(m_(2))=(z-z_(2))/(n_(2))`
Intersect if
`|(x_(2)-x_(1),y_(2)-y_(1),z_(2)-z_(1)),(l_(1),m_(1),n_(1)),(l_(2),m_(2),n_(2))|=0`
So given lines will intersect, if
`|(3-1,k+1,0-1),(2,3,4),(l,2,1)|=0`
`implies 2(3-8)-(k+1)(2-4)-(4-3)=0impliesk=9/2`
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OBJECTIVE RD SHARMA ENGLISH-PLANE AND STRAIGHT LINE IN SPACE -Section I - Solved Mcqs
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