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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)                   
    • \ The angle between the planes is \[{{0}^{o}}.\]


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