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A line is drawn from the point P(1, 1, 1) and perpendicular to a line with direction ratios $(1, 1, 1)$ to intersect the plane $x + 2 y + 3 z = 4$ at Q. The locus of point Q is

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$\frac{x}{1} = \frac{y - 5}{- 2} = \frac{z + 2}{1}$

$\frac{x}{- 2} = \frac{y - 5}{1} = \frac{z + 2}{1}$

$x = y = z$

$\frac{x}{2} = \frac{y}{3} = \frac{z}{5}$

answer is A.

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Detailed Solution

Locus of Q is the line of intersection of the plane $x + 2 y + 3 z = 4$ and

$1 (x - 1) + 1 (y - 1) + 1 (z - 1) = 0 \Rightarrow then line is \frac{x}{1} = \frac{y - 5}{- 2} = \frac{z + 2}{1}$

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