Question

If $\mathbf{a} = \mathbf{i} + 2\mathbf{j} + 3\mathbf{k},\mathbf{b} = - \mathbf{i} + 2\mathbf{j} + \mathbf{k}$ and $\mathbf{c} = 3\mathbf{i} + \mathbf{j},$ then the unit vector along its resultant is

• A. $3\mathbf{i} + 5\mathbf{j} + 4\mathbf{k}$
• B. $\frac{3\mathbf{i} + 5\mathbf{j} + 4\mathbf{k}}{50}$
• C. $\frac{3\mathbf{i} + 5\mathbf{j} + 4\mathbf{k}}{5\sqrt{2}}$
• D. None of these

Answer 1

Answer: (C)

$\frac{3\mathbf{i} + 5\mathbf{j} + 4\mathbf{k}}{5\sqrt{2}}$

Answer 2

$\mathbf{R} = 3\mathbf{i} + 5\mathbf{j} + 4\mathbf{k} \Rightarrow \widehat{\mathbf{R}} = \frac{3\mathbf{i} + 5\mathbf{j} + 4\mathbf{k}}{5\sqrt{2}}.$