Question

The equation of straight line passing through the point $(a,b,c)$ and parallel to $Z$-axis is

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

Answer 1

Answer: (D)

The equation of line passing through $(a,b,c)$ is
$\frac{x-a}{1}=\frac{y-b}{m}=\frac{z-c}{n}=\lambda$
Since, the line is parallel to $Z$-axis, therefore any point on this line will be of the form $\left(a,b,z_1\right)$.
Now, from Eq. (i) any point on the line is $(\lambda +a,\lambda m+b,\lambda n+c)$
$\therefore \lambda +a=a\to 1=0,\lambda =0$
$\to \lambda m+b=b\to m=0,\lambda =0$
$\to \lambda n+c=z_1\to z_1=c(\because \lambda =0)$
$\to 1^2+m^2+n^2=1$
$\to 0+0+n^2=1$
$\to n=1$
Hence, the equation of line is
$\frac{x-a}{0}=\frac{y-b}{0}=\frac{z-c}{1}$