Let a → , b → and c → be three non - coplanar unit vectors such that the angle between every pair of them is π 3 . If a → × b → + b → × c → = p a → + q b → + r c → , where p, q and r are scalars, then

Question

Let a → , b → and c → be three non - coplanar unit vectors such that the angle between every pair of them is π 3 . If a → × b → + b → × c → = p a → + q b → + r c → , where p, q and r are scalars, then the value of p 2 + 2 q 2 + r 2 q 2 is _______

TestHub · Accepted Answer

a → = b → = c → = 1 a → × b → + b → × c → = p a → + q b → + r c → a → . b → × c → = p + q a → . b → + r a → . c → And a → b → c → = 1 2 p + q 2 + r 2 = a → b → c → .......(i) p 2 + q + r 2 = 0 ......(ii) p 2 + q 2 + r = a → b → c → ......(iii) ⇒ p = r = - q p 2 + 2 q 2 + r 2 q 2 = 4

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