JEE Main & Advanced Mathematics Vector Algebra Question Bank Application of vectors in three dimensional geometry

  • question_answer
    The position vectors of two points P and Q are \[3\mathbf{i}+\mathbf{j}+2\mathbf{k}\] and \[\mathbf{i}-2\mathbf{j}-4\mathbf{k}\] respectively. The equation of the plane through Q and perpendicular to PQ is

    A)            \[\mathbf{r}.(2\mathbf{i}+3\mathbf{j}+6\mathbf{k})=28\]

    B)            \[\mathbf{r}.(2\mathbf{i}+3\mathbf{j}+6\mathbf{k})=32\]

    C)            \[\mathbf{r}.(2\mathbf{i}+3\mathbf{j}+6\mathbf{k})+28=0\]

    D)            None of these

    Correct Answer: C

    Solution :

               The required plane is \[\{\mathbf{r}-(\mathbf{i}-2\mathbf{j}-4\mathbf{k})\}.\overrightarrow{PQ}=0\].


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