JEE Main & Advanced
Mathematics
Vector Algebra
Question Bank
Critical Thinking
question_answer
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]
A)\[{{0}^{o}}\]
B)\[\frac{\pi }{4}\]
C)\[\frac{\pi }{3}\]
D)\[\frac{\pi }{2}\]
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)