Class 12

Math

3D Geometry

Three Dimensional Geometry

The line which passes through the origin and intersect the two lines x−12=y+34=z−53,x−42=y+33=z−144, is

- x1=y−3=z5
- x−1=y3=z5
- x1=y3=z−5
- x1=y4=z−5

**Correct Answer: ** Option(a)

**Solution: **[a] Let the line be xa=yb=zc (i) If line (i) intersects with the line x−12 =y+34=z−53, Then ∣∣∣∣a24b4−3c314∣∣∣∣=0⇒9a−7b−10c=0 (ii) From (i) and (ii), we have a1=b−3=c5 ∴ The line is x1=y−3=z5