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

Options

A. ` - 2 `
B. ` - 5 `
C. ` 5 `
D. ` 2 `

Answer

B

Explanation

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 ] `
` rArr k ( - 2k - 2 ) - 2 ( - 6 - 2 ) + 3 ( 3 - k) = 0 `
` rArr 2 k ^ 2 + 5 k - 25 = 0 `
` rArr ( 2 k - 5 ) ( k + 5 ) = 0 `
` rArr k = ( 5) / (2 ) , - 5 `
Hence, integer value of k is ` - 5`.