Let a → , b → , c → be three non-zero, non-coplanar vectors and p → , q → , r → be three vectors given by p → = a → + 2 b → - 2 c → , q → = 3 a → + b → - 3 c → and r → = a → - 4 b → + 4 c → . If the volume of parallelepiped determined by a → , b → and c → is v 1 cubic units and volume of tetrahedron determined by p → , q → and r → is v 2 cubic units, then v 1 v 2 is equal to

Question

Let a → , b → , c → be three non-zero, non-coplanar vectors and p → , q → , r → be three vectors given by p → = a → + 2 b → - 2 c → , q → = 3 a → + b → - 3 c → and r → = a → - 4 b → + 4 c → . If the volume of parallelepiped determined by a → , b → and c → is v 1 cubic units and volume of tetrahedron determined by p → , q → and r → is v 2 cubic units, then v 1 v 2 is equal to, 1 3, 3 4, 1 4, 1 2

MARKS App · Accepted Answer

v 1 = a → b → c → v 2 = 1 6 p → q → r → = 1 6 1 2 - 2 3 1 - 3 1 - 4 4 a → b → c → v 2 = 1 6 1 4 - 12 - 2 12 + 3 - 2 - 12 - 1 a → b → c → v 2 = 1 6 - 8 - 30 + 26 a → b → c → v 2 = 2 a → b → c → v 1 v 2 = 1 2 = 0.5

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