Question

Find the equation of the straight line passing through the points $(2,3,4)$ and $(1,-2,3)$

• A. $\frac{x-2}{1}=\frac{y-3}{-5}=\frac{z-4}{-1}$
• B. $\frac{x-2}{-1}=\frac{y-3}{-5}=\frac{z-4}{-1}$
• C. $\frac{x-2}{-1}=\frac{y-3}{5}=\frac{z-4}{-1}$
• D. $\frac{x-2}{-1}=\frac{y-3}{-5}=\frac{z-4}{1}$

Answer 1

The correct option is B $\frac{x-2}{-1}=\frac{y-3}{-5}=\frac{z-4}{-1}$

The straight line passing through a point $(a,b,c)$ and parallel to the direction $(i,j,k)$ is written as $\frac{x-a}{i}=\frac{y-b}{j}=\frac{z-c}{k}$

Similarly, here the direction ratio would be given by $(2-1,3-(-2),4-3)$ i.e. $(1,5,1)$

Thus, the line equation can be written as $\frac{x-2}{-1}=\frac{y-3}{-5}=\frac{z-4}{-1}$