The area of parallelogram formed by vectors P = 2i - j + 5k and Q = 3i - 2j + 4k is (a) √(72) (b) √(86) (c) √(104) (d) √(240)

Answer: (b). Area of parallelogram = |P × Q|. P × Q = i[(-1)(4) - (5)(-2)] - j[(2)(4) - (5)(3)] + k[(2)(-2) - (-1)(3)] = 6i + 7j - k |P × Q| = √(36 + 49 + 1) = √(86) So the answer is (b) √(86).

The area of parallelogram formed by vectors P = 2i - j + 5k and Q =… | MHT CET 2026 (20 Apr, Shift 1)

Q1MHT CET 2026 · 20 APR · SHIFT 1Medium

Vector (Cross) Product

The area of parallelogram formed by vectors $\vec{P} = 2\hat{i} - \hat{j} + 5\hat{k}$ and $\vec{Q} = 3\hat{i} - 2\hat{j} + 4\hat{k}$ is

Show answer and solution

Answer: (b)

Area of parallelogram $= |\vec{P} \times \vec{Q}|$ .
$\vec{P} \times \vec{Q} = \hat{i}[(-1)(4) - (5)(-2)] - \hat{j}[(2)(4) - (5)(3)] + \hat{k}[(2)(-2) - (-1)(3)]$
$= 6\hat{i} + 7\hat{j} - \hat{k}$
$|\vec{P} \times \vec{Q}| = \sqrt{36 + 49 + 1} = \sqrt{86}$
So the answer is (b) $\sqrt{86}$ .

Report a mistake

Vector (Cross) Product question from MHT CET 2026 (20 Apr, Shift 1)

More questions on Vector (Cross) Product