JEE Main 2010 Mathematics question

Statement-1: The point A(3, 1, 6) is the mirror image of the point B(1, 3, 4) in the plane x − y + z = 5. Statement-2: The plane x − y + z = 5 bisects the line segment joining A(3, 1, 6) and B(1, 3, 4).

(1)Statement-1 is true, Statement-2 is true; Statement-2 is not the correct explanation for Statement-1Correct
(2)Statement-1 is true, Statement-2 is false
(3)Statement-1 is false, Statement-2 is true
(4)Statement-1 is true, Statement-2 is true; Statement-2 is the correct explanation for Statement-1

Answer: (1)

Solution

The midpoint (2, 2, 5) satisfies 2 − 2 + 5 = 5, so the plane bisects AB (Statement 2 true). Also is parallel to the normal (1, −1, 1), so AB is perpendicular to the

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Question ID VK-039287