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JEE 2023 Mathematics PYQ — Let the vectors represent three coterminal edges of a parallelepi… | Mathem Solvex | Mathem Solvex

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JEE 2023 — Mathematics PYQ

JEE | Mathematics | 2023

Let the vectors $a, b, c$ represent three coterminal edges of a parallelepiped of volume $V$ . Then the volume of the parallelepiped, whose coterminal edges are represented by $a + b + c$ and $a + 2 b + 3 c$ is equal to:

Choose the correct answer:

A.
2V
B.
6V
C.
3V
D.
V
(Correct Answer)

Correct Answer:

Explanation

Volume of parallelopiped
$[a b c]$
$v_{1} = [a b + c, a + 2 b + 3 c]$

$v_{1} = 101 am p; 0 am p; 1 am p; 2 am p; 0 am p; 0 am p; 3 [a b c]$
$v_{1} = (3 - 0) V$

Explanation

Volume of parallelopiped
$[a b c]$
$v_{1} = [a b + c, a + 2 b + 3 c]$

$v_{1} = 101 am p; 0 am p; 1 am p; 2 am p; 0 am p; 0 am p; 3 [a b c]$
$v_{1} = (3 - 0) V$

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