Vector Algebra Question 229
Question: The unit vector parallel to the resultant vector of $ 2\mathbf{i}+4\mathbf{j}-5\mathbf{k} $ and $ \mathbf{i}+2\mathbf{j}+3\mathbf{k} $ is
[MP PET 2003]
Options:
A) $ \frac{1}{7},(3\mathbf{i}+6\mathbf{j}-2\mathbf{k}) $
B) $ \frac{\mathbf{i}+\mathbf{j}+\mathbf{k}}{\sqrt{3}} $
C) $ \frac{\mathbf{i}+\mathbf{j}+2\mathbf{k}}{\sqrt{6}} $
D) $ \frac{1}{\sqrt{69}},(-\mathbf{i}-\mathbf{j}+8\mathbf{k}) $
Show Answer
Answer:
Correct Answer: A
Solution:
- Resultant vector $ =(2\mathbf{i}+4\mathbf{j}-5\mathbf{k})+(\mathbf{i}+2\mathbf{j}+3\mathbf{k})=3\mathbf{i}+6\mathbf{j}-2\mathbf{k} $ Unit vector $ =\frac{3\mathbf{i}+6\mathbf{j}-2\mathbf{k}}{\sqrt{9+36+4}}=\frac{1}{7}(3\mathbf{i}+6\mathbf{j}-2\mathbf{k}) $ .
BETA
