JEE Main · 2023 · 06 Apr 2023 · Shift 2 · Vector Algebra

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

Answer: (C)

Solution

The volume of a parallelopiped with edges

a, b, c

V = [a b c]

. The new volume is

[a, b + c, a + 2 b + 3 c]

. Express this as a determinant:

101012013 [a b c] = 1 (3 - 2) V = V

JEE Main · 2023 · 06 Apr 2023 · Shift 2 · Single correct option