The direction ratios of the normal to the plane passing through th | Filo
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3D Geometry

Three Dimensional Geometry

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The direction ratios of the normal to the plane passing through the points (1, -2, 3), (-1, 2, -1) and parallel to x−22=y+13=z4 is

  1. (2, 3, 4)
  2. (14, 0, 7)
  3. (-2, 0, -1)
  4. (2, 0, -1)
Correct Answer: Option(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 A−8−6=B4−4=C3+4 ⇒A−14=B0=C7⇒A:B:C=2:0:−1
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