Question

If O be the origin and the position vector of A be $4\mathbf{i} + 5\mathbf{j},$ then a unit vector parallel to $\overset{\rightarrow}{OA}$ is

• A. $\frac{4}{\sqrt{41}}\mathbf{i}$
• B. $\frac{5}{\sqrt{41}}\mathbf{i}$
• C. $\frac{1}{\sqrt{41}}(4\mathbf{i} + 5\mathbf{j})$
• D. $\frac{1}{\sqrt{41}}(4\mathbf{i} - 5\mathbf{j})$

Answer 1

Answer: (C)

$\frac{1}{\sqrt{41}}(4\mathbf{i} + 5\mathbf{j})$

Answer 2

Unit vector prarallel to $\overset{\rightarrow}{OA}$ $= \frac{4\mathbf{i} + 5\mathbf{j}}{\sqrt{16 + 25}} = \frac{1}{\sqrt{41}}(4\mathbf{i} + 5\mathbf{j}).$