The angle made by a vector B = 3i + 2j + 4k with Y axis is (a) cos ⁻¹((4)/(√(11))) (b) cos ⁻¹((3)/(√(17))) (c) cos ⁻¹((2)/(√(29))) (d) cos ⁻¹((5)/(√(23)))

Answer: (c). Direction cosine with Y axis: cos β = (By)/(|B|). |B| = √(9 + 4 + 16) = √(29) cos β = (2)/(√(29)) ⇒ β = cos ⁻¹((2)/(√(29))) So the answer is (c).

The angle made by a vector B = 3i + 2j + 4k with Y axis is | MHT CET 2026 (15 May, Shift 2)

Q5MHT CET 2026 · 15 MAY · SHIFT 2Easy

Vector Basics, Unit Vectors & Components

The angle made by a vector $\vec{B} = 3\hat{i} + 2\hat{j} + 4\hat{k}$ with Y axis is

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Answer: (c)

Direction cosine with Y axis: $\cos\beta = \frac{B_y}{|\vec{B}|}$ .
$|\vec{B}| = \sqrt{9 + 4 + 16} = \sqrt{29}$
$\cos\beta = \frac{2}{\sqrt{29}} \Rightarrow \beta = \cos^{-1}\left(\frac{2}{\sqrt{29}}\right)$
So the answer is (c).

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