Vector Algebra Question 348
Question: If the position vectors of the points A, B, C, D be $ \mathbf{i}+\mathbf{j}+\mathbf{k},2,\mathbf{i}+5,\mathbf{j},3,\mathbf{i}+2,\mathbf{j}-3\mathbf{k} $ and $ \mathbf{i}-6,\mathbf{j}-\mathbf{k}, $ then the angle between the vectors $ \overrightarrow{AB} $ and $ \overrightarrow{CD} $ is
Options:
A) $ \frac{\pi }{4} $
B) $ \frac{\pi }{3} $
C) $ \frac{\pi }{2} $
D) $ \pi $
Show Answer
Answer:
Correct Answer: D
Solution:
- $ \overrightarrow{AB}=\mathbf{i}+4\mathbf{j}-\mathbf{k}, $ $ \overrightarrow{CD}=-2\mathbf{i}-8\mathbf{j}+2\mathbf{k} $ $ \cos \theta =\frac{\overrightarrow{AB}.\overrightarrow{CD}}{|\overrightarrow{AB}|.|\overrightarrow{CD}|}=\frac{-2-32-2}{\sqrt{18}.\sqrt{72}} $ $ =\frac{-2-32-2}{2\times 18}=-1\Rightarrow \theta =\pi . $
BETA
