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

Step-by-step solution

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 →