JEE Main · 2019 · 11 Jan 2019 · Shift 2 · Three Dimensional Geometry

Two lines

\frac{x - 3}{1} = \frac{y + 1}{3} = \frac{z - 6}{- 1}

and

\frac{x + 5}{7} = \frac{y - 2}{- 6} = \frac{z - 3}{4}

intersect at the point

R

. The reflection of

R

in the

x y

-plane has coordinates:

(A) $(2, - 4, - 7)$ ✓ Correct
(B) $(2, 4, 7)$
(C) $(2, - 4, 7)$
(D) $(- 2, 4, 7)$

Answer: (A)

Solution

A general point on the first line is

(λ + 3, 3 λ - 1, - λ + 6)

and on the second

(7 μ - 5, - 6 μ + 2, 4 μ + 3)

. Equating the

x

and

y

coordinates gives

λ = 7 μ - 8

and

3 λ = - 6 μ + 3

; substituting,

21 μ - 24 = - 6 μ + 3

, so

μ = 1

and

λ = - 1

. The point of intersection is

R (2, - 4, 7)

, and reflecting it in the

x y

-plane flips the sign of

z

to give

(2, - 4, - 7)

JEE Main · 2019 · 11 Jan 2019 · Shift 2 · Single correct option

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