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JEE Main & Advanced Mathematics Three Dimensional Geometry Question Bank Self Evaluation Test - Introduction to Three Dimensional Geometry

  • question_answer
    If the origin is shifted (1, 2 -3) without changing the directions of the axis, then find the new coordinates of the point (0, 4, 5) with respect to new frame.

    A) (-1, 2, 8)

    B) (4, 5, 1)

    C) (3, -2, 4)

    D) (6, 0, 8)

    Correct Answer: A

    Solution :

    [a] In the new frame \[x'=x-{{x}_{1}},\,\,y'=y-{{y}_{1}},\] \[z'=z-{{z}_{1}},\] where \[\left( {{x}_{1}},{{y}_{1}},{{z}_{1}} \right)\] is shifted origin. \[\Rightarrow x'=0-1=-1=y'=4-2=2=2,\]             \[z'=5+3=8\] Hence, the coordinated of the point with respect to the new coordinated frame are (-1, 2, 8)


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