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MHT CET 2025 (23 Apr, Shift 1) · Scalar (Dot) Product

Scalar (Dot) Product question from MHT CET 2025 (23 Apr, Shift 1)

Q14MHT CET 2025 · 23 APR · SHIFT 1Medium

Scalar (Dot) Product

If $\vec{P} = b\hat{i} + 6\hat{j} + \hat{k}$ and $\vec{Q} = \hat{i} - a\hat{j} + 4\hat{k}$ are perpendicular to each other, also $3b - a = 5$ . The value of $a$ and $b$ is

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Answer: (b)

Perpendicular: $b - 6a + 4 = 0 \Rightarrow b = 6a - 4$ .
Put in $3b - a = 5$ : $18a - 12 - a = 5 \Rightarrow a = 1$ .
$b = 6 - 4 = 2$
So the answer is (b) $a = 1,\ b = 2$ .

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