If A = (1, 1, 1), B = (2, -1, 3), C = (0, 4, -2), D = (1, 2, ) and AB, AC and AD are coplanar then is

JEE Advanced Mathematics question

If , , , and , and are coplanar then is

(A)
(B)Correct
(C)
(D)

Answer: (B)

Solution

The direction ratios are ; ; . All three lines pass through . They are coplanar exactly when some direction (the normal to the common plane) is perpendicular to all three:

l - 2m + 2n = 0, -l + 3m - 3n = 0, 0· l +

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Question ID VK-109805