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

  • question_answer
    If \[\vec{a},\text{ }\vec{b},\text{ }\vec{c},\text{ }\vec{d}\] are the position vectors of points A, B, C and D respectively such that \[(\vec{a}-\vec{d}).(\vec{b}-\vec{c})=(\vec{b}-\vec{d}).(\vec{c}-\vec{a})=0\] then D is the

    A) Centroid of \[\Delta \text{ }ABC\]

    B) Circumcentre of \[\Delta \,ABC\]

    C) Orthocentre of \[\Delta \,ABC\]

    D) None of these  

    Correct Answer: C

    Solution :

    [c] \[\therefore \,(\overset{\to }{\mathop{a}}\,-\overset{\to }{\mathop{d}}\,)(\overset{\to }{\mathop{b}}\,-\overset{\to }{\mathop{c}}\,)=0\] \[\Rightarrow \overrightarrow{DA}\] and \[\overrightarrow{CB}\] are perpendicular \[(\overset{\to }{\mathop{b}}\,-\overset{\to }{\mathop{d}}\,)\cdot (\overset{\to }{\mathop{c}}\,-\overset{\to }{\mathop{a}}\,)=0\] \[\Rightarrow \,\,\overrightarrow{DB}\] and \[\overrightarrow{AC}\] are perpendicular \[\therefore \]      D is orthocenter of \[\Delta ABC\]


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