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JEE Main & Advanced Mathematics Vector Algebra Question Bank Self Evaluation Test - Vector Algebra

  • question_answer
    If \[\vec{a}\] is a position vector of a point (1, -3) and A is another point (-1, 5), then what are the coordinates of the point B such that\[\overrightarrow{AB}=\vec{a}\]?

    A) (2, 0)

    B) (0, 2)

    C) (-2, 0)

    D) (0, -2)

    Correct Answer: B

    Solution :

    [b] Let the coordinates of B be (x, y). \[\overset{\to }{\mathop{a}}\,=i-3j\] P.V. of A is (-1, 5 ) so, \[\overrightarrow{OA}=i+5j,\] \[\overrightarrow{OB}=xi+yj,\] \[\therefore \overrightarrow{AB}=\overrightarrow{OB}-\overrightarrow{OA}=\overrightarrow{a}\] \[\Rightarrow (x+1)\hat{i}+(y-5)\hat{j}=\hat{i}-3\hat{j}\] \[\Rightarrow x+1=1\] and \[y-5=-3\] \[\Rightarrow x=0\] and \[y=2\] \[\therefore \]      Coordinates of B are (0, 2 ).


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