If lines and and third line passing through form a triangle of area units

MATHEMATICS · Single correct · CBSE · Mathematics · Three-Dimensional Geometry · Three-Dimensional Geometry

Problem

If lines

x = y = z

and

x = \frac{y}{2} = \frac{z}{3}

and third line passing through

(1, 1, 1)

form a triangle of area

\sqrt{6}

units, then point of intersection of third line with second line will be (1)

(1, 2, 3)

(2)

(2, 4, 6)

(3)

\left(\frac{4}{3}, \frac{8}{3}, \frac{12}{3}\right)

(4) None of these