Vector Algebra Question 143
Question: The vectors b and c are in the direction of north-east and north-west respectively and |b|=|c|= 4. The magnitude and direction of the vector d = c - b, are
[Roorkee 2000]
Options:
A) $ 4\sqrt{2}, $ towards north
B) $ 4\sqrt{2} $ , towards west
C) 4, towards east
D) 4, towards south
Show Answer
Answer:
Correct Answer: B
Solution:
- Clearly, $ \mathbf{b}\bot \mathbf{c} $ ,
$ \therefore $ $ \mathbf{b}.\mathbf{c}=0 $
Now, $ \mathbf{d}=\mathbf{c}-\mathbf{b}\Rightarrow |\mathbf{d}{{|}^{2}}=|\mathbf{c}-\mathbf{b}{{|}^{2}} $
= $ |\mathbf{c}{{|}^{2}}+|\mathbf{b}{{|}^{2}}-2\mathbf{b},.,\mathbf{c}=16+16-0 $
Þ $ |d|=\sqrt{32}=4\sqrt{2} $ and direction of d is west.
BETA
