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JEE Main & Advanced Mathematics Three Dimensional Geometry Question Bank Critical Thinking

  • question_answer
    A square \[ABCD\] of diagonal 2a is folded along the diagonal \[AC\] so that the planes \[DAC\] and \[BAC\] are at right angle. The shortest distance between \[DC\] and \[AB\] is [Kurukshetra CEE 1998]

    A) \[\sqrt{2}a\]

    B) \[2a/\sqrt{3}\]

    C) \[2a/\sqrt{5}\]

    D) [(\sqrt{3}/2)a\]

    Correct Answer: B

    Solution :

    • When folded co-ordinates will be \[D\,(0,\,\,0,\,\,a);\,\,C\,(a,\,0,\,0);\]           
    • \[A(-a,\,\,0,\,\,0);\,\,B\,(0,\,\,-a,\,\,0)\]           
    • Equation \[DC\text{ is, }\frac{x}{a}=\frac{y}{0}=\frac{z-a}{-a}\]           
    • Equation \[AB\,\,\text{is,}\,\,\frac{x+a}{a}=\frac{y}{-a}=\frac{z}{0}\] \[\therefore \] Shortest distance \[=\frac{2a}{\sqrt{3}}\,\],  (By formula).


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