2. Questions Bank
  3. JEE Main & Advanced
  4. Mathematics
  5. Three Dimensional Geometry

JEE Main & Advanced Mathematics Three Dimensional Geometry Question Bank Self Evaluation Test - Three Dimensional Geometry

  • question_answer
    The direction ratios of the normal to the plane passing through the points (1, -2, 3), (-1, 2, -1) and parallel to \[\frac{x-2}{2}=\frac{y+1}{3}=\frac{z}{4}\] is

    A) (2, 3, 4)

    B) (14, 0, 7)

    C) (-2, 0, -1)

    D) (2, 0, -1)

    Correct Answer: D

    Solution :

    [d] Any plane through (1, -2, -3) is \[A(x-1)+B(y+2)+C(z-3)=0\]                   (1) The point \[(-1,2,-1)\] lies in this plane if \[-2A+4B-4C=0\] i.e., if \[A-2B+2C=0\]                 (2) The plane (1) is parallel to the given line with d. r., 2, 3, 4 if \[2A+3B+4C=0\]                   (3) From (2) and (3), we have \[\frac{A}{-8-6}=\frac{B}{4-4}=\frac{C}{3+4}\] \[\Rightarrow \frac{A}{-14}=\frac{B}{0}=\frac{C}{7}\Rightarrow A:B:C=2:0:-1\]


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