If A = i + j + 3k, B = -i + j + 4k and C = 2i - 2j - 8k, then the angle between the vectors P = A + B + C and Q = (A × B) is (in degree) (a) 0° (b) 45° (c) 90° (d) 60°

Answer: (c). P = A + B + C = 2i + 0j - k. Q = A × B = i(4 - 3) - j(4 + 3) + k(1 + 1) = i - 7j + 2k. P · Q = 2 + 0 - 2 = 0, so P ⊥ Q. So the answer is (c) 90°.

If A = i + j + 3k, B = -i + j + 4k and C = 2i - 2j - 8k, then the… | MHT CET 2025 (20 Apr, Shift 1)

Q6MHT CET 2025 · 20 APR · SHIFT 1Medium

Vector (Cross) Product

If $\vec{A} = \hat{i} + \hat{j} + 3\hat{k}, \ \vec{B} = -\hat{i} + \hat{j} + 4\hat{k}$ and $\vec{C} = 2\hat{i} - 2\hat{j} - 8\hat{k}$ , then the angle between the vectors $\vec{P} = \vec{A} + \vec{B} + \vec{C}$ and $\vec{Q} = (\vec{A} \times \vec{B})$ is (in degree)

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Answer: (c)

$\vec{P} = \vec{A} + \vec{B} + \vec{C} = 2\hat{i} + 0\hat{j} - \hat{k}$ .
$\vec{Q} = \vec{A} \times \vec{B} = \hat{i}(4 - 3) - \hat{j}(4 + 3) + \hat{k}(1 + 1) = \hat{i} - 7\hat{j} + 2\hat{k}$ .
$\vec{P} \cdot \vec{Q} = 2 + 0 - 2 = 0$ , so $\vec{P} \perp \vec{Q}$ .
So the answer is (c) $90^\circ$ .

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Vector (Cross) Product question from MHT CET 2025 (20 Apr, Shift 1)

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