The angles made by the vector vec{A} = 2hat{i | vedclass

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(B) Given vector $\vec{A} = 2\hat{i} + 3\hat{j}$.Magnitude of vector $\vec{A}$ is $|\vec{A}| = \sqrt{2^2 + 3^2} = \sqrt{4 + 9} = \sqrt{13}$.The angle

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$\cos^{-1}(2/\sqrt{13}), \cos^{-1}(3/\sqrt{13})$

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(B) Given vector $\vec{A} = 2\hat{i} + 3\hat{j}$.Magnitude of vector $\vec{A}$ is $|\vec{A}| = \sqrt{2^2 + 3^2} = \sqrt{4 + 9} = \sqrt{13}$.The angle $\alpha$ with the $x$-axis is given by $\cos \alpha = \frac{A_x}{|\vec{A}|} = \frac{2}{\sqrt{13}}$, so $\alpha = \cos^{-1}(2/\sqrt{13})$.The angle $\beta$ with the $y$-axis is given by $\cos \beta = \frac{A_y}{|\vec{A}|} = \frac{3}{\sqrt{13}}$, so $\beta = \cos^{-1}(3/\sqrt{13})$.Thus, the angles are $\cos^{-1}(2/\sqrt{13})$ and $\cos^{-1}(3/\sqrt{13})$.

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

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