Two lines (x-3)/1 = (y+1)/3 = (z-6)/(-1) and (x+5)/7 = (y-2)/(-6) = (z-3)/4 intersect at the point R. The reflection of R in the xy-plane has coordinates

Two lines (x-3)/1 = (y+1)/3 = (z-6)/(-1) and (x+5)/7 =… — JEE Main 2019 Mathematics PYQ

JEE Main 2019 · 11 Jan · Shift II

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

xy

-plane has coordinates

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

Show answer and solution

Correct option: A

Solution

Parametrize the first line: x = 3+t, y = -1+3t, z = 6-t.
Parametrize the second line: x = -5+7s, y = 2-6s, z = 3+4s.

Setting equal: 3+t = -5+7s → t = -8+7s; -1+3t = 2-6s → 3(-8+7s)-1 = 2-6s → 21s-25 = 2-6s → 27s = 27 → s = 1, t = -1.

Point R: x = 3+(-1) = 2, y = -1+3(-1) = -4, z = 6-(-1) = 7. So R = (2, -4, 7).

Reflection in the xy-plane negates the z-coordinate: (2, -4, -7).

[JEE Main 2019 · 11 Jan · Shift II]

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