Vector Algebra Question 140
Question: If $ \mathbf{a}=\mathbf{i}+2\mathbf{j}+2\mathbf{k} $ and $ \mathbf{b}=3\mathbf{i}+6\mathbf{j}+2\mathbf{k}, $ then a vector in the direction of a and having magnitude as |b| is
[IIT 1983]
Options:
A) $ 7,(\mathbf{i}+\mathbf{j}+\mathbf{k}) $
B) $ \frac{7}{3},(\mathbf{i}+2\mathbf{j}+2\mathbf{k}) $
C) $ \frac{7}{9},(\mathbf{i}+2\mathbf{j}+2,\mathbf{k}) $
D) None of these
Show Answer
Answer:
Correct Answer: B
Solution:
- $ |\mathbf{b}|\mathbf{\hat{a}}=\sqrt{9+36+4}( \frac{\mathbf{i}+2\mathbf{j}+2\mathbf{k}}{\sqrt{1+4+4}} )=\frac{7}{3}(\mathbf{i}+2\mathbf{j}+2\mathbf{k}). $
BETA
