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MHT CET 2025 (5 May, Shift 2) · Scalar (Dot) Product

Scalar (Dot) Product question from MHT CET 2025 (5 May, Shift 2)

Q13MHT CET 2025 · 5 MAY · SHIFT 2Medium

Scalar (Dot) Product

Two vectors $a\hat{i} + b\hat{j} + \hat{k}$ and $2\hat{i} - 3\hat{j} + 4\hat{k}$ are perpendicular to each other. When $3a + 2b = 7$ , the ratio of $a$ to $b$ is $\frac{x}{2}$ . The value of $x$ is

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Answer: (c)

Perpendicular: $2a - 3b + 4 = 0$ ; also $3a + 2b = 7$ .
Solving: $a = 1$ , $b = 2$ .
$\frac{a}{b} = \frac{1}{2} = \frac{x}{2} \Rightarrow x = 1$
So the answer is (c) 1.

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