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) $45°$
Concept. The angle with the $x$-axis follows from the direction cosine $\cos\alpha = \dfrac{R_x}{|\vec R|}$.
Step 1. Sum. $\vec A + \vec B = 5\hat i - 4\hat j + 3\hat k$, magnitude $\sqrt{50} = 5\sqrt2$.
Step 2. Angle. $\cos\alpha = \dfrac{5}{5\sqrt2} = \dfrac{1}{\sqrt2} \Rightarrow \alpha = 45°$.
Answer. $45°$ (Option B).
Solution by Sreeraj P, M.Sc Physics