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JEE Advanced2014MathematicsVector AlgebraActual

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 _______

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Step-by-step solution

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 =

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