Question

The equation of a line passing through (1,2,3) having direction ratios 1,2,4 is .

• A. $\frac{x-1}{1}=\frac{y-2}{2}=\frac{z-3}{3}=r$
• B. $\frac{x-1}{2}=\frac{y-2}{1}=\frac{z-4}{3}=r$
• C. $\frac{x-1}{1}=\frac{y-2}{2}=\frac{z-4}{3}=r$
• D. $\frac{x-1}{1}=\frac{y-2}{2}=\frac{z-3}{4}=r$

Answer 1

The correct option is D $\frac{x-1}{1}=\frac{y-2}{2}=\frac{z-3}{4}=r$

The DRs of the line segment joining any two points on the line are proportional to the DRs of the line. We know that (1,2,3) lies on the line and the DRs are 1,2,4. So, if (x,y,z) is a general point on the line, then

$\frac{x-1}{1}=\frac{y-2}{2}=\frac{z-3}{4}=r$