The vector P = ai + aj + 3k and Q = ai - 2j - k are perpendicular to each other. Then positive value of ' a ' is (a) 3 (b) 4 (c) 9 (d) 13

Answer: (a). Perpendicular: P · Q = 0. a² - 2a - 3 = 0 ⇒ (a - 3)(a + 1) = 0 Positive value: a = 3, answer (a).

The vector P = ai + aj + 3k and Q = ai - 2j - k are perpendicular to… | MHT CET 2026 (13 May, Shift 2)

Q3MHT CET 2026 · 13 MAY · SHIFT 2Easy

Scalar (Dot) Product

The vector $\vec{P} = a\hat{i} + a\hat{j} + 3\hat{k}$ and $\vec{Q} = a\hat{i} - 2\hat{j} - \hat{k}$ are perpendicular to each other. Then positive value of ' $a$ ' is

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Answer: (a)

Perpendicular: $\vec{P} \cdot \vec{Q} = 0$ .
$a^2 - 2a - 3 = 0 \Rightarrow (a - 3)(a + 1) = 0$
Positive value: $a = 3$ , answer (a).

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Scalar (Dot) Product question from MHT CET 2026 (13 May, Shift 2)

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