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JEE Main & Advanced JEE Main Paper (Held On 9 April 2016)

  • question_answer
    In a triangle ABC, right angled at the vertex A, if the position vectors of A, B and C are respectively \[3\hat{i}+\hat{j}-\hat{k},-\hat{i}+3\hat{j}+p\hat{k}\]and\[5\hat{i}+q\hat{j}-4\hat{k},\]then the point (p, q) lies on a line   JEE Main Online Paper (Held On 09 April 2016)

    A) parallel to y-axis

    B) making an acute angle with the positive direction of x-axis

    C) parallel to x-axis

    D) making an obtuse angle with the position direction of x-axis.

    Correct Answer: B

    Solution :

                    \[\overrightarrow{AB}=-4i+2j+(p+1)\hat{k}\]                 \[\overrightarrow{AC}=2\hat{i}+(q-1)\hat{j}-3\hat{k}\]                 \[\overrightarrow{AB}.\overrightarrow{AC}=0\]\[\Rightarrow \]\[-8+2(9-1)-3(p+1)=0\] \[\Rightarrow \]\[-3p+2q-13=0\]\[\Rightarrow \]\[(p,q)\]lies on line \[3x-2y+13=0\] Slope \[=\frac{3}{2}\]


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