Let the vectors a → , b → , c → represent three coterminous edges of a parallelopiped of volume V . Then the volume of the parallelopiped, whose coterminous edges are represented by a → , b → + c → and a → + 2 b → + 3 c → is equal to

Step-by-step solution

We know that, Volume of parallelepiped whose edges determined by vectors a → ,   b → ,   c → is a → b → c → . Now it is given that V is volume of parallelepiped a → ,   b → ,   c → , so required volume of parallelepiped with new edges will be = a → b → + c → a → + 2 b → + 3 c → = 1 0 0 0 1 1 1 2 3 a → b → c → = 1 3 - 2 - 0 + 0 a → b → c → = a → b → c → =