2. Sample Papers
  3. JEE Main & Advanced

JEE Main & Advanced Sample Paper JEE Main - Mock Test - 20

  • question_answer
    If M denotes the mid-point of the line joining \[A(4\hat{i}+5\hat{j}-10\hat{k})\] and \[B(-\hat{i}+2\hat{j}+\hat{k}),\] then equation of the plane through At and perpendicular to AB, is

    A) \[\widehat{r}.(-5\hat{i}-3\hat{j}+11\hat{k})+\frac{135}{2}=0\]

    B)        \[\widehat{r}.\left( \frac{3}{2}\hat{i}+\frac{7}{2}\hat{j}-\frac{9}{2}\hat{k} \right)+\frac{35}{2}=0\]

    C)        \[\widehat{r}.(4\hat{i}+5\hat{j}-\hat{k})+4=0\]

    D)        \[\widehat{r}.(-\hat{i}+2\hat{j}+\hat{k})+4=0\]

    Correct Answer: A

    Solution :

    Mid-point M of AB is \[\left( \frac{1}{2}(4\hat{i}+5\hat{j}-10\hat{k}-\hat{i}+2\hat{j}+\hat{k} \right)=\left( \frac{3}{2}\hat{i}+\frac{7}{2}\hat{j}-\frac{9}{2}\hat{k} \right)\] Also, \[\overrightarrow{AB}=-\hat{i}+2\hat{j}+\hat{k}-(4\hat{i}+5\hat{j}-10\hat{k})\] \[=-5\hat{i}-3\hat{j}+11\hat{k}\] So, the plane passing through M and perpendicular to the \[\overrightarrow{AB}\] is \[\left[ \overrightarrow{r}-\left( \frac{3}{2}\hat{i}+\frac{7}{2}\hat{j}-\frac{9}{2}\hat{k} \right) \right].(-5\hat{i}-3\hat{j}+11\hat{k})=0\] \[\Rightarrow \,\,\overrightarrow{r}.(-5\hat{i}-3\hat{j}+11\hat{k})+\frac{135}{2}=0.\]


You need to login to perform this action.
You will be redirected in 3 sec spinner