JEE Main · 2019 · 09 Jan 2019 · Shift 1 · Three Dimensional Geometry

The equation of line passing through

(- 4, 3, 1)

, parallel to the plane

x + 2 y - z - 5 = 0

and intersecting the line

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

is:

Answer: (C)

Solution

With the point

(- 4, 3, 1)

, a general point of the given line is

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

, so the joining direction is

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

. Parallelism to the plane requires this

⊥ (1, 2, - 1)

(3 - 3 t) + 2 (2 t) - (1 - t) = 2 + 2 t = 0 \Rightarrow t = - 1

, giving direction

(6, - 2, 2) ∥ (3, - 1, 1)

, which meets the given line at

(2, 1, 3)

. Hence the line is

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

JEE Main · 2019 · 09 Jan 2019 · Shift 1 · Single correct option