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

  • question_answer
    The co-ordinates of the point which divides the join of the points (2, ?1, 3) and (4, 3, 1) in the ratio 3 : 4 internally are given by [MP PET 1997]

    A)            \[\frac{2}{7},\frac{20}{7},\frac{10}{7}\]

    B)            \[\frac{15}{7},\frac{20}{7},\frac{3}{7}\]

    C)            \[\frac{10}{7},\frac{15}{7},\frac{2}{7}\]

    D)            \[\frac{20}{7},\frac{5}{7},\frac{15}{7}\]

    Correct Answer: D

    Solution :

               From \[x=\frac{{{m}_{1}}{{x}_{2}}+{{m}_{2}}{{x}_{1}}}{{{m}_{1}}+{{m}_{2}}},\,\,y=\frac{{{m}_{1}}{{y}_{2}}+{{m}_{2}}{{y}_{1}}}{{{m}_{1}}+{{m}_{2}}}\],            \[z=\frac{{{m}_{1}}{{z}_{2}}+{{m}_{2}}{{z}_{1}}}{{{m}_{1}}+{{m}_{2}}}\];  \[x=\frac{20}{7},\,\,y=\frac{5}{7},\,\,z=\frac{15}{7}.\]


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