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

If the straight lines `(x-1)/k=(y-2)/2=(z-3)/3` and `(x-2)/3=(y-3)/k=(z-1)/2` intersect at a point, then the integer k is equal to (1) `-5` (2) 5 (3) 2 (4) `-2`

A

`-2`

B

`-5`

C

5

D

2

Text Solution

Verified by Experts

The correct Answer is:
B
since, two lines intersect at a point. Then shortest distance between them is zero.
`therefore|(k,2,3),(3,k,2),(1,1,-2)|=0`
`[because|(a_(1),b_(1),c_(1)),(a_(2),b_(2),c_(2)),(x_(2)-x_(1),y_(2)-y_(1),z_(2)-z_(1))|=0]`
`impliesk(-2k-2)-2(-6-2)`
`+3(3-k)=0`
`implies2k^(2)+5k-25=0`
`implies(2k-5)(k+5)=0`
`impliesk=(5)/(2)-5`
Hence, integer value of k is -5.
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