Vector Algebra Question 327
If θ be the angle between the unit vectors a and b, then $ \cos \frac{\theta }{2}= $
[MP PET 1998; Pb. CET 2002]
Options:
A) $ \frac{1}{2},|\mathbf{a}-\mathbf{b}| $
B) $ \frac{1}{2},|\mathbf{a}+\mathbf{b}| $
C) $ \frac{|\mathbf{a}-\mathbf{b}|}{|\mathbf{a}+\mathbf{b}|} $
D) $ \frac{|\mathbf{a}+\mathbf{b}|}{|\mathbf{a}-\mathbf{b}|} $
Show Answer
Answer:
Correct Answer: B
Solution:
($\mathbf{a}+\mathbf{b}).(\mathbf{a}+\mathbf{b})=,|\mathbf{a}{{|}^{2}}+|\mathbf{b}{{|}^{2}}+,2\mathbf{a},.,\mathbf{b}$ or $|\mathbf{a}+\mathbf{b}{{|}^{2}}=2{{\cos }^{2}}\frac{\theta }{2}\Rightarrow \cos \frac{\theta }{2}=\frac{1}{2}|\mathbf{a}+\mathbf{b}|.$
BETA
