Question

Given $\mathbf{a} = \mathbf{i} + \mathbf{j} - \mathbf{k},\mathbf{b} = - \mathbf{i} + 2\mathbf{j} + \mathbf{k}$ and $\mathbf{c} = - \mathbf{i} + 2\mathbf{j} - \mathbf{k}.$ A unit vector perpendicular to both $\mathbf{a} + \mathbf{b}$ and $\mathbf{b} + \mathbf{c}$ is

• A. i
• B. j
• C. k
• D. $\frac{\mathbf{i} + \mathbf{j} + \mathbf{k}}{\sqrt{3}}$

Answer 1

Answer: (C)

k

Answer 2

Obviously, $\mathbf{b} + \mathbf{c} = - 2\mathbf{i} + 4\mathbf{j}$ and $\mathbf{a} + \mathbf{b} = 3\mathbf{j}.$

Hence the unit vector $\mathbf{k}$ is perpendicular to both $\mathbf{b} + \mathbf{c}$ and $\mathbf{a} + \mathbf{b}.$