JEE Main · 2008 · 27 Apr 2008 · Offline · Three Dimensional Geometry

If the straight lines

\frac{x - 1}{k} = \frac{y - 2}{2} = \frac{z - 3}{3}

and

\frac{x - 2}{3} = \frac{y - 3}{k} = \frac{z - 1}{2}

intersect at a point, then the integer k is equal to

(A)-5✓ Correct
(B)5
(C)2
(D)-2

Answer: (A)

Solution

Two lines meet only if the vector joining a point on one to a point on the other lies in the plane of their direction vectors, which makes the determinant of those three vectors vanish. Forming it with direction ratios

(k, 2, 3)

and

(3, k, 2)

and the join

(1, 1, - 2)

and expanding gives

2 k^{2} + 5 k - 25 = 0

, whose roots are

k = - 5

and

k = \frac{5}{2}

. Only the integer root is admissible, so

k = - 5

JEE Main · 2008 · 27 Apr 2008 · Offline · Single correct option

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