Vector Algebra Question 15
Question: Let $\vec{b}=3 \hat{j}+4 \hat{k}, \vec{a}=\hat{i}+\hat{j}$ and let $\vec{b}_1$ and $\vec{b}_2$ be component of vector b parallel and perpendicular to $\vec{a}$. If $\vec{b}_1=\frac{3}{2} \hat{i}+\frac{3}{2} \hat{j}$ then $\vec{b}_2$ is equal to
[MP PET 1989]
Options:
A) $\frac{3}{2} \hat{i}+\frac{3}{2} \hat{j}+4 \hat{k}$
B) $-\frac{3}{2} \hat{i}+\frac{3}{2} \hat{j}+4 \hat{k}$
C) $-\frac{3}{2} \hat{i}+\frac{3}{2} \hat{j}$
D) None of these
Show Answer
Answer:
Correct Answer: B
Solution:
- $ {{\mathbf{b}}_2}=\mathbf{b}-{{\mathbf{b}}_1}=-\frac{3}{2}\mathbf{i}+\frac{3}{2}\mathbf{j}+4\mathbf{k} $ and obviously $ {{\mathbf{b}}_2} $
is perpendicular to $ \mathbf{a}. $
BETA
