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J & K CET Engineering J and K - CET Engineering Solved Paper-2011

  • question_answer
    The position vector of two given points A and B are \[4i-3j-k\]and \[5i-5j+k\]respectively. If y is the angle between AB and z-axis, then \[\cos \,\gamma \] is equal to

    A)  \[1/3\]  

    B)  \[2/3\]  

    C)  \[-2/3\]

    D)  \[0\]

    Correct Answer: D

    Solution :

    Given, position vector of A and B are, \[OA=4i-3j-k\] \[OB=5i-5j+k\] \[\Rightarrow \] \[AB=OB-OA\] \[=(5i-5j+k)-(4i-3j-k)\] \[=(i-2j)\] Position vector of z-axis is let \[OC=(0i+0j+k)\] Given, angle between AB and OC (z-axis) is r. \[\Rightarrow \] \[\cos \gamma =\frac{AB.OC}{|AB||OC|}=\frac{(i-2j).k}{\sqrt{1+4}.\sqrt{1}}=\frac{0}{\sqrt{5}}=0\] \[\Rightarrow \] \[\cos \,\gamma =0\]


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