A plane which passes through the point (3, 2, 0) and the line x-4 1 = y-7 5 = z-4 4 is

JEE Main 2002 Mathematics question

A plane which passes through the point and the line is

(1)x - y + z = 1Correct
(2)x + y + z = 5
(3)x + 2y - z = 1
(4)2x - y + z = 5

Answer: (1)

Solution

The plane must contain the point (3, 2, 0), the point (4, 7, 4) of the line, and be parallel to the direction (1, 5, 4). Check (1) : (3, 2, 0): ✓; (4, 7, 4): ✓; normal (1, −1, 1)·(1, 5, 4) ✓. So

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Question ID VK-038056