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JEE Main & Advanced Mathematics Three Dimensional Geometry Question Bank System of Co-ordinates, Direction cosines and direction ratios, Projection

  • question_answer
    If the co-ordinates of A and B be (1, 2, 3) and (7, 8, 7), then the projections of the line segment AB on the co-ordinate axes are

    A)            6, 6, 4

    B)            4, 6, 4

    C)            3, 3, 2

    D)            2, 3, 2

    Correct Answer: A

    Solution :

               Here, \[{{x}_{2}}-{{x}_{1}}=6\], \[{{y}_{2}}-{{y}_{1}}=6\], \[{{z}_{2}}-{{z}_{1}}=4\] and d.c's of \[x,\,y,\,z\]-axes are (1,0,0), (0,1,0), (0, 0, 1) respectively. Now projection = \[({{x}_{2}}-{{x}_{1}})l+({{y}_{2}}-{{y}_{1}})m+({{z}_{2}}-{{z}_{1}})n\] \[\therefore \] Projections of line AB on co-ordinate axes are 6, 6, 4 respectively.


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