Let L 1 : x - 2 2 = y - 3 - 1 = z - 1 3 , L 2 : x - 2 - 1 = y - 3 3 = z - 1 5 3 and L 3 : x - 2 - 32 = y - 3 - 19 = z - 1 15 are three lines intersecting each other at the point P and a given plane at A , B , C respectively, such that P A = 2 , P B = 3 , P C = 6 . The volume (in cubic units) of the tetrahedron P A B C is

Question

Let L 1 : x - 2 2 = y - 3 - 1 = z - 1 3 , L 2 : x - 2 - 1 = y - 3 3 = z - 1 5 3 and L 3 : x - 2 - 32 = y - 3 - 19 = z - 1 15 are three lines intersecting each other at the point P and a given plane at A , B , C respectively, such that P A = 2 , P B = 3 , P C = 6 . The volume (in cubic units) of the tetrahedron P A B C is, 2, 18, 6, 10

MARKS App · Accepted Answer

∵ All three lines are perpendicular ⇒ Volume of the tetrahedron = 1 6 P A × P B × P C = 1 6 × 2 × 3 × 6 = 6 cubic units

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