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

  • question_answer
    The distance between the planes given by \[\mathbf{r}.(\mathbf{i}+2\mathbf{j}-2\mathbf{k})+5=0\] and \[\mathbf{r}.(\mathbf{i}+2\mathbf{j}-2\mathbf{k})-8=0\] is

    A)            1 unit

    B)            \[\frac{13}{3}\] unit

    C)            13 unit

    D)            None of these

    Correct Answer: B

    Solution :

               The two planes are on the opposite side of the origin. Therefore, if \[{{p}_{1}}\] and \[{{p}_{2}}\] are the lengths of the perpendicular from the origin to the planes \[\mathbf{r}.(\mathbf{i}+2\mathbf{j}-2\mathbf{k})+5=0\] and \[\mathbf{r}.(\mathbf{i}+2\mathbf{j}-2\mathbf{k})-8=0\] respectively, then the required distance is given by \[{{p}_{1}}+{{p}_{2}}=\frac{5}{3}+\frac{8}{3}=\frac{13}{3}\]unit.


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