Question

The unit vector parallel to the resultant vector of $2\mathbf{i} + 4\mathbf{j} - 5\mathbf{k}$ and $\mathbf{i} + 2\mathbf{j} + 3\mathbf{k}$ is

• A. $\frac{1}{7}(3\mathbf{i} + 6\mathbf{j} - 2\mathbf{k})$
• B. $\frac{\mathbf{i} + \mathbf{j} + \mathbf{k}}{\sqrt{3}}$
• C. $\frac{\mathbf{i} + \mathbf{j} + 2\mathbf{k}}{\sqrt{6}}$
• D. $\frac{1}{\sqrt{69}}( - \mathbf{i} - \mathbf{j} + 8\mathbf{k})$

Answer 1

Answer: (A)

$\frac{1}{7}(3\mathbf{i} + 6\mathbf{j} - 2\mathbf{k})$

Answer 2

Resultant vector

$= (2\mathbf{i} + 4\mathbf{j} - 5\mathbf{k}) + (\mathbf{i} + 2\mathbf{j} + 3\mathbf{k}) = 3\mathbf{i} + 6\mathbf{j} - 2\mathbf{k}$

Unit vector $= \frac{3\mathbf{i} + 6\mathbf{j} - 2\mathbf{k}}{\sqrt{9 + 36 + 4}} = \frac{1}{7}(3\mathbf{i} + 6\mathbf{j} - 2\mathbf{k})$.