The angle made by vector A = 2i + 3j with x-axis and that with y-axis are respectively. (a) tan ⁻¹ 2√(13) tan ⁻¹ 3√(13) (b) cos ⁻¹(2)/(√(13)) cos ⁻¹(3)/(√(13)) (c) cos ⁻¹1/√(2) cos ⁻¹1/√(3) (d) sin ⁻¹1/√(6) sin ⁻¹(1)/(2√(3))

Answer: (b). |A| = √(4 + 9) = √(13) With x-axis: cos α = (2)/(√(13)); with y-axis: cos β = (3)/(√(13)) So the answer is (b) cos ⁻¹(2)/(√(13)), cos ⁻¹(3)/(√(13)).

The angle made by vector A = 2i + 3j with x-axis and that with y-axis… | MHT CET 2026 (18 Apr, Shift 1)

Q6MHT CET 2026 · 18 APR · SHIFT 1Easy

Vector Basics, Unit Vectors & Components

The angle made by vector $\vec{A} = 2\hat{i} + 3\hat{j}$ with x-axis and that with y-axis are respectively.

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Answer: (b)

$|\vec{A}| = \sqrt{4 + 9} = \sqrt{13}$
With x-axis: $\cos\alpha = \frac{2}{\sqrt{13}}$ ; with y-axis: $\cos\beta = \frac{3}{\sqrt{13}}$
So the answer is (b) $\cos^{-1}\frac{2}{\sqrt{13}},\ \cos^{-1}\frac{3}{\sqrt{13}}$ .

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