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

  • question_answer
    The foot of the perpendicular from the point (1, 6, 3) to the line \[\frac{x}{1}=\frac{y-1}{2}=\frac{z-2}{3}\] is

    A) (1, 2, 5)

    B) (-1, -1, -1)

    C) (2, 5, 8)

    D) (-2, -3, -4)

    Correct Answer: A

    Solution :

    [a] Equation of line is \[\frac{x}{1}=\frac{y-1}{2}=\frac{z-2}{3}\] Any point on this line is \[(K,2K+1,3K+2.)\] if this is the foot of perpendicular form (1, 6, 3) then d. r of this perpendicular are \[<K-1,2K-5,3K-1>\] Now, using condition of perpendicularly we have \[(K-1)1+(2K-5)2+(3K-1)3=0\] \[\Rightarrow K-1+4K-10+9K-3=0\Rightarrow K=1\] Hence, required foot of perpendicular is \[(1,3,5)\]


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