Question

If the position vectors of the points A, B, C, D be $2\mathbf{i} + 3\mathbf{j} + 5\mathbf{k},$ $\mathbf{i} + 2\mathbf{j} + 3\mathbf{k}, - 5\mathbf{i} + 4\mathbf{j} - 2\mathbf{k}$ and $\mathbf{i} + 10\mathbf{j} + 10\mathbf{k}$ respectively, then

• A. $\overset{\rightarrow}{AB} = \overset{\rightarrow}{CD}$
• B. $\overset{\rightarrow}{AB}||\overset{\rightarrow}{CD}$
• C. $\overset{\rightarrow}{AB}\bot\overset{\rightarrow}{CD}$
• D. None of these

Answer 1

Answer: (B)

$\overset{\rightarrow}{AB}||\overset{\rightarrow}{CD}$

Answer 2

$\overset{\rightarrow}{AB} = - \mathbf{i} - \mathbf{j} - 2\mathbf{k}$ and $\overset{\rightarrow}{CD} = 6\mathbf{i} + 6\mathbf{j} + 12\mathbf{k}$

Hence, $\overset{\rightarrow}{AB}||\overset{\rightarrow}{CD}.$