Let u → , v → and w → be vectors in three-dimensional space, where u → and v → are unit vectors which are not perpendicular to each other and u → · w → = 1 ,   v → · w → = 1 ,   w → · w → = 4 . If the volume of the parallelopiped, whose adjacent sides are represented by the vectors u → , v → and w → , is 2 , then the value of | 3 u → + 5 v → | is
A. A
Volume of the parallelopiped is u → v → w → = 2 ⇒ u → v → w → 2 = 2 ⇒ u → · u → u → · v u → · w → v → · u → v → · v → v → · w → w → · u → w → · v → w → · w → = 2 Using u → · w → = 1 ,   v → · w → = 1 ,   w → · w → = 4 , we get u → · u → u → · v u → · w → v → · u → v → · v → v → · w → w → · u → w → · v → w → · w → = 1 u → · v → 1 v → · u → 1 1 1 1 4 = 2 ⇒ 3 - u → · v → 4 u → · v → - 1 + v → · u → - 1 = 2 ⇒ u → · v → ( 1 - 4 u → · v → + 1 ) = 0 ⇒ u → · v → = 1 2    ( ∵ u → · v → ≠ 0 ) Also, u → = 1 ,   v → = 1 So, | 3 u → + 5 v → | = | 3 u → + 5 v → | 2 = 9 u → 2 + 25 v → 2 + 30 u → · v → = 7
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