Question

The volume of a parallelopiped determined by the vectors a, b and c is 5. Find the volume of the parallelopiped determined by the vectors 3(a + b), (b + c) and 2(c + a).

Answer 1

Given [a, b, c] = 5

Now, [3 (a + b), (b + c), 2 (c + a)]

= 3.2[(a + b), (b + c), 2(c + a)]

= 6[(a + b), (b + c), 2(c + a)]

= 6 × 2[a, b, c]

= 6 × 2 × 5

= 60.