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J & K CET Engineering J and K - CET Engineering Solved Paper-2013

  • question_answer
    If \[(3,\,4,-1)\] and \[(-1,\,2,3)\] be end points of the diameter of a sphere, then the radius of the sphere is

    A)  \[2\]                     

    B)  \[3\]

    C)  \[6\]                     

    D)  \[7\]

    Correct Answer: B

    Solution :

    We know that, Centre is the mid- point of the diameter of any sphere. \[\therefore \]   Coordinate of the centre of the sphere \[=\left( \frac{3+(-1)}{2},\,\frac{4+2}{2},\,\frac{-1+3}{2} \right)\] \[=(1,\,3,\,1)\] \[\therefore \] length of the radius  = Distance between the Points \[(1,3,1)\] and \[(-1,2,3)\] \[=\sqrt{{{(1+1)}^{2}}+{{(3-2)}^{2}}+{{(1-3)}^{2}}}\] \[=\sqrt{4+1+4}=\sqrt{9}=3\]


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