JEE Main 2012 Mathematics question

Statement 1: If the points (1, 2, 2), (2, 1, 2) and (2, 2, z) and (1, 1, 1) are coplanar, then z = 2. Statement 2: If the 4 points P, Q, R and S are coplanar, then the volume of the tetrahedron PQRS is 0.

(1)Statement 1 is false,, Statement 2 is true.Correct
(2)Statement 1 is true, Statement 2 is false.
(3)Statement 1 is true, Statement 2 is true, Statement 2 is a correct explanation of Statement 1.
(4)Statement 1 is true, Statement 2 is true, Statement 2 is not a correct explanation of Statement 1.

Answer: (1)

Solution

Vectors from (1, 1, 1): (0, 1, 1), (1, 0, 1), (1, 1, z − 1). Coplanar ⇔

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Question ID VK-103531