JEE Main · MathematicsHard

$Find the image of the point (1, 2, 3) in the plane x + y + z = 6 .$

Show correct answer & step-by-step solution

Correct answer: A — $(2, 3, 4)$

Solution

Using \frac{x ^{'} - 1}{1} = \frac{y ^{'} - 2}{1} = \frac{z ^{'} - 3}{1} = - 2 \frac{1 + 2 + 3 - 6}{1 ^{2} + 1 ^{2} + 1 ^{2}} = 0 . Thus x^{'} = 1, y^{'} = 2, z^{'} = 3 is wrong; re-evaluating: the point is on the plane, so the image is the point itself.

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