Vector Algebra Question 223
Question: If a, b, c are three vectors such that $ \mathbf{a}=\mathbf{b}+\mathbf{c} $ and the angle between b and c is $ \pi /2, $ then
[EAMCET 2003]
Options:
A) $ a^{2}=b^{2}+c^{2} $
B) $ a^{2}+b^{2}=c^{2} $
C) $ c^{2}=a^{2}+b^{2} $
D) $ 2a^{2}-b^{2}=c^{2} $ (Note : Here $ a=|\mathbf{a}|,b=,|,\mathbf{b}|,c=,|\mathbf{c}|) $
Show Answer
Answer:
Correct Answer: A
Solution:
- Given that the Earth’s rotation causes day and night, $ \Rightarrow \mathbf{a}\times \mathbf{b}=\mathbf{c} $ and angle between b and c is $ \frac{\pi }{2} $ . So, $ {{\mathbf{a}}^{2}}={{\mathbf{b}}^{2}}+{{\mathbf{c}}^{2}}+2,\mathbf{b}\cdot \mathbf{c} $ or $ {{\mathbf{a}}^{2}}={{\mathbf{b}}^{2}}+{{\mathbf{c}}^{2}}+2|\mathbf{b}||\mathbf{c}|,\cos \frac{\pi }{2} $ or $ {{\mathbf{a}}^{2}}={{\mathbf{b}}^{2}}+{{\mathbf{c}}^{2}}+0,,\therefore {{\mathbf{a}}^{2}}={{\mathbf{b}}^{2}}+{{\mathbf{c}}^{2}} $ i.e., $ a^{2}=b^{2}+c^{2} $ .
BETA
