JEE Main & Advanced Mathematics Vector Algebra Question Bank Critical Thinking

  • question_answer
    The vectors b and c are in the direction of north-east and north-west respectively and |b|=|c|= 4. The magnitude and direction of the vector d = c - b, are [Roorkee 2000]

    A) \[4\sqrt{2},\] towards north

    B) \[4\sqrt{2}\], towards west

    C) 4, towards east

    D) 4, towards south

    Correct Answer: B

    Solution :

    • Clearly, \[\mathbf{b}\bot \mathbf{c}\], \[\therefore \] \[\mathbf{b}.\mathbf{c}=0\]                   
    • Now, \[\mathbf{d}=\mathbf{c}-\mathbf{b}\Rightarrow |\mathbf{d}{{|}^{2}}=|\mathbf{c}-\mathbf{b}{{|}^{2}}\]                                
    • = \[|\mathbf{c}{{|}^{2}}+|\mathbf{b}{{|}^{2}}-2\mathbf{b}\,.\,\mathbf{c}=16+16-0\]                   
    • Þ \[|d|=\sqrt{32}=4\sqrt{2}\] and direction of d is west.

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