Question

The equation of a straight line parallel to the $x$-axis is given by

• A. $\frac{x-a}{1}=\frac{y-b}{1}=\frac{z-c}{1}$
• B. $\frac{x-a}{0}=\frac{y-b}{1}=\frac{z-c}{1}$
• C. $\frac{x-a}{0}=\frac{y-b}{0}=\frac{z-c}{1}$
• D. $\frac{x-a}{1}=\frac{y-b}{0}=\frac{z-c}{0}$

Answer 1

Answer: (D)

$\frac{x-a}{1}=\frac{y-b}{0}=\frac{z-c}{0}$

The straight line parallel to the x-axis will make the angles $0^{\circ }$, ${90}^{\circ }$ and ${90}^{\circ }$ with the x, y and z-axis respectively.

so, the direction cosines of the straight line are

$l=cos{0}^{\circ }=1$

$m=cos{90}^{\circ }=0$

$n=cos{90}^{\circ }=0$

If the straight line passes through a point $(a,b,c)$ and having direction cosines $l,m,n$ , the equation of line is

$\frac{x-a}{l}=\frac{y-b}{m}=\frac{z-c}{n}$

$\frac{x-a}{1}=\frac{y-b}{0}=\frac{z-c}{0}$