Vector Algebra Question 278
Question: If $ \mathbf{a}=\mathbf{i}-\mathbf{j} $ and $ \mathbf{b}=\mathbf{i}+\mathbf{k} $ , then a unit vector coplanar with a and b and perpendicular to a is
Options:
A) i
B) j
C) k
D) None of these
Show Answer
Answer:
Correct Answer: D
Solution:
- $ \mathbf{c}=\lambda \mathbf{a}+\mu \mathbf{b}=(\lambda +\mu )\mathbf{i}-\lambda \mathbf{j}+\mu \mathbf{k} $ Now, $ \mathbf{c}.\mathbf{a}=0\Rightarrow 2\lambda +\mu =0\Rightarrow \mu =-2\lambda $ Therefore, $ \mathbf{c}=-\lambda \mathbf{i}-\lambda \mathbf{j}-2\lambda \mathbf{k}=(\sqrt{6})(-\lambda )[ \frac{\mathbf{i}+\mathbf{j}+2\mathbf{k}}{\sqrt{6}} ] $ Hence, unit vector $ =\frac{(\mathbf{i}+\mathbf{j}+2\mathbf{k})}{\sqrt{6}} $ .
BETA
