Q 11-03-007NEETJEE MainEAMCET 2007 (Medical)Easy
Given two vectors $\vec{A} = \hat{i} - 2\hat{j} - 3\hat{k}$ and $\vec{B} = 4\hat{i} - 2\hat{j} + 6\hat{k}$. The angle made by $(\vec{A} + \vec{B})$ with the $x$-axis is
Answer: (B) $45°$
$$\vec{A} + \vec{B} = 5\hat{i} - 4\hat{j} + 3\hat{k}, \qquad |\vec{A} + \vec{B}| = \sqrt{25 + 16 + 9} = 5\sqrt{2}$$
The direction cosine with the $x$-axis is
$$\cos\alpha = \frac{5}{5\sqrt{2}} = \frac{1}{\sqrt{2}} \;\Rightarrow\; \alpha = 45°$$
Solution by Sreeraj P, M.Sc Physics