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Let a → ,   b → and c → be three non-zero non-coplanar vectors and p → ,   q → and r → be three vectors defined as p → = a → + b → − 2 c → ;   q → = 3 a → - 2 b → + c →   and   r → = a → - 4 b → + 2 c → If the volume of parallelepiped determined by a → ,   b → &#1

Correct answer

15

Step-by-step solution

Given, [ a ⃗ b ⃗ c ⃗ ] = V 1 [ p ⃗ q ⃗ r ⃗ ] = | 1 1 − 2 3 − 2 + 1 1 − 4 2 | [ a ⃗ b ⃗ c ⃗ ] = [ 1 ( − 4 + 4 ) − 1 ( 6 − 1 ) − 2 ( − 12 + 2 ) ] V 1 V 2 = ( − 5 + 20 ) V 1 = 15 V 1   ⇒ K = 15

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