Question

If the position vectors of A and B are $\mathbf{i} + 3\mathbf{j} - 7\mathbf{k}$ and $5\mathbf{i} - 2\mathbf{j} + 4\mathbf{k},$ then the direction cosine of $\overset{\rightarrow}{AB}$ along y-axis is

• A. $\frac{4}{\sqrt{162}}$
• B. $- \frac{5}{\sqrt{162}}$
• C. – 5
• D. 11

Answer 1

Answer: (B)

$- \frac{5}{\sqrt{162}}$

Answer 2

$\overset{\rightarrow}{AB} = 4\mathbf{i} - 5\mathbf{j} + 11\mathbf{k}$

Direction cosine along $y -$axis

$= \frac{- 5}{\sqrt{16 + 25 + 121}} = \frac{- 5}{\sqrt{162}}.$