The line passing through the points $(5,1, a)$ and $(3, b, 1)$ crosses the yz-plane at the point $\left(0, \frac{17}{2}, \frac{-13}{2}\right)$. Then

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

The line passing through the points

(5, 1, a)

and

(3, b, 1)

crosses the yz-plane at the point

(0, \frac{17}{2}, \frac{- 13}{2})

. Then

(A) $a = 2, b = 8$
(B) $a = 4, b = 6$
(C) $a = 6, b = 4$ ✓ Correct
(D) $a = 8, b = 2$

Answer: (C)

Solution

Parametrise the line through

(5, 1, a)

and

(3, b, 1)

so that

x = 5 - 2 λ

. It crosses the

y z

-plane where

x = 0

, i.e.

λ = \frac{5}{2}

. The

y

-coordinate there,

1 + λ (b - 1) = \frac{17}{2}

, solves to

b = 4

, and the

z

-coordinate,

a + λ (1 - a) = - \frac{13}{2}

, solves to

a = 6

. Hence

a = 6

and

b = 4

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

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