Vector Algebra Question 170
Question: Let the vectors a, b, c and d be such that $ (\mathbf{a}\times \mathbf{b})\times (\mathbf{c}\times \mathbf{d})=0 $ . Let $ P_1 $ and $ P_2 $ be planes determined by pair of vectors a, b and c, d respectively. Then the angle between $ P_1 $ and $ P_2 $ is
[IIT Screening 2000; MP PET 2004]
Options:
A) $ 0^{o} $
B) $ \frac{\pi }{4} $
C) $ \frac{\pi }{3} $
D) $ \frac{\pi }{2} $
Show Answer
Answer:
Correct Answer: A
Solution:
- A vector perpendicular to the plane $ P_1 $ of a, b is $ \mathbf{a}\times \mathbf{b} $
A vector perpendicular to the plane $ P_2 $ of c, d is $ \mathbf{c}\times \mathbf{d} $ .
Þ $ (\mathbf{a}\times \mathbf{b})\times (\mathbf{c}\times \mathbf{d})=0 $
Þ (a × b) || (c × d)
\ The angle between the planes is $ 0^{o}. $
BETA
