Vector Algebra Question 360
Question: If $ \mathbf{a}=\mathbf{i}+2\mathbf{j}-3\mathbf{k} $ and $ \mathbf{b}=3\mathbf{i}-\mathbf{j}+2\mathbf{k}, $ then the angle between the vectors $ \mathbf{a}+\mathbf{b} $ and $ \mathbf{a}-\mathbf{b} $ is
[Karnataka CET 1994; Orissa JEE 2005]
Options:
A) $ 30^{o} $
B) $ 60^{o} $
C) $ 90^{o} $
D) x
Show Answer
Answer:
Correct Answer: C
Solution:
- We have $ \mathbf{a}+\mathbf{b}=4\mathbf{i}+\mathbf{j}-\mathbf{k} $ and $ \mathbf{a}-\mathbf{b}=-2\mathbf{i}+3\mathbf{j}-5\mathbf{k}. $ Clearly $ (\mathbf{a}+\mathbf{b}),.,(\mathbf{a}-\mathbf{b})=0. $ Hence $ (\mathbf{a}+\mathbf{b}),\bot ,(\mathbf{a}-\mathbf{b}). $
BETA
