JEE Main · 2012 · 29 Apr 2012 · Offline · Three Dimensional Geometry

If the lines

\frac{x - 1}{2} = \frac{y + 1}{3} = \frac{z - 1}{4}

and

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

intersect, then

k

is equal to

(A)-1
(B) $\frac{2}{9}$
(C) $\frac{9}{2}$ ✓ Correct
(D)0

Answer: (C)

Solution

Points on the first line can be written

(2 t + 1, 3 t - 1, 4 t + 1)

and on the second

(s + 3, 2 s + k, s)

. Matching the

x

- and

z

-coordinates gives

2 t + 1 = s + 3

and

4 t + 1 = s

; substituting the second into the first yields

2 t + 1 = 4 t + 4

, so

t = - \frac{3}{2}

and then

s = - 5

. For the lines to meet, the

y

-coordinates must also agree:

3 t - 1 = 2 s + k

gives

- \frac{11}{2} = - 10 + k

, so

k = \frac{9}{2}

JEE Main · 2012 · 29 Apr 2012 · Offline · Single correct option

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