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Suppose that p → , q → a n d r → are three non - coplanar vectors in R 3 . Let the components of a vector s → along (p, q ) and (r ) be 4,3 and 5 respectively. If the components of - p → + q → + r → , p → - q → + r → a n d - p → - q → + r → are x, y and z, respectively, then the value of 2 x + y + z is

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This question is seem to be wrong but may be taken as S → = x - p → + q → + r → + y p → - q → + r → + z - p → - q → + r → - x + y - z = 4 ..... (i) x - y - z = 3 ...... (ii) x + y + z = 5 ..... (iii) Add (i) and (ii) - 2 z = 7 ⇒ z = - 7 2 2 x = 8 ⇒ x = 4 2 x + y + z = 2 4 + 1 = 9

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