Vector Algebra Question 354
Question: The angle between the vectors $ \mathbf{i}-\mathbf{j}+\mathbf{k} $ and $ \mathbf{i}+2\mathbf{j}+\mathbf{k} $ is
[BIT Ranchi 1991]
Options:
A) $ {{\cos }^{-1}}( \frac{1}{\sqrt{15}} ) $
B) $ {{\cos }^{-1}}( \frac{4}{\sqrt{15}} ) $
C) $ {{\cos }^{-1}}( \frac{4}{15} ) $
D) $ \frac{\pi }{2} $
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Answer:
Correct Answer: D
Solution:
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$ (\mathbf{i}-\mathbf{j}+\mathbf{k})\,.\,(\mathbf{i}+2\mathbf{j}+\mathbf{k})=\sqrt{3}\sqrt{6}\cos \theta $
$ \Rightarrow \cos \theta =\frac{0}{\sqrt{3}\sqrt{6}}\Rightarrow \theta =\frac{\pi }{2}. $
BETA
