Class 12

Math

3D Geometry

Three Dimensional Geometry

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

- (2, 3, 4)
- (14, 0, 7)
- (-2, 0, -1)
- (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