JEE Main 2022 Mathematics question
A plane P is parallel to two lines whose direction rations are −2, 1, −3 and −1, 2, −2 and it contains the point (2, 2, −2). Let P intersect the co-ordinate axes at the points A, B, C making the intercepts , , . If V is the volume of the tetrahedron OABC, where O is the origin and , then the ordered pair (V, p) is equal to
Answer: (2)
Solution
The normal of the plane is the cross product of the direction vectors (−2, 1, −3) and (−1, 2, −2): = (1·(−2) − (−3)(2), (−3)(−1) − (−2)(−2), (−2)(2) − (1)(−1)) = (4, −1, −3). The plane through (2, 2, −2) is 4(x − 2) − (y −
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