Vector Algebra Question 25
Question: If $\vec{a}=2 \hat{i}+\hat{j}+2 \hat{k}$ and $\vec{b}=5 \hat{i}-3 \hat{j}+\hat{k}$, then the projection of $\vec{b}$ on $\vec{a}$ is
[Karnataka CET 2002]
Options:
A) 3
B) 4
C) 5
D) 6
Show Answer
Answer:
Correct Answer: A
Solution:
- Vectors $ a=2i+j+2k $ and $ \mathbf{b}=5i-3j+k $ . We know that the projection of b on $ a=\frac{b,.,a}{|\mathbf{a}|}=\frac{(2i+j+2k),.,(5i-3j+k)}{\sqrt{{{(2)}^{2}}+{{(1)}^{2}}+{{(2)}^{2}}}}=\frac{10-3+2}{\sqrt{9}}=\frac{9}{3}=3. $
BETA
