Vector Algebra Question 377
Question: The angle between the vectors a + b and a ? b, when $ \mathbf{a}=(1,,1,,4) $ and $ b=(1,,-1,,4) $ is
[Karnataka CET 2003]
Options:
A) $ 90^{o} $
B) $ 45^{o} $
C) $ 30^{o} $
D) $ 15^{o} $
Show Answer
Answer:
Correct Answer: A
Solution:
- $ \mathbf{a}=(1,,1,,4)=\mathbf{i}+\mathbf{j}+4\mathbf{k}, $ $ \mathbf{b}=(1,,-1,,4)=\mathbf{i}-\mathbf{j}+4\mathbf{k} $ \ $ \mathbf{a}+\mathbf{b}=2\mathbf{i}+8\mathbf{k} $
Þ $ \mathbf{a}-\mathbf{b}=2\mathbf{j} $ Since, $ (\mathbf{a}+\mathbf{b}),.,(\mathbf{a}-\mathbf{b})=0 $ \ $ (\mathbf{a}+\mathbf{b})\bot (\mathbf{a}-\mathbf{b}) $ . Hence $ \theta =90{}^\circ $ .
BETA
