Question

Find the Cartesian equation of the line parallel to y-axis and passing through the point (1, 1, 1).

Answer 1

DC's of a line parallel to y axis are $(0,1,0)$

Equation of a line passing through $(x_1,y_1,z_1)$ having DC's as $(a,b,c)$ is given by

$\frac{x-x_1}{a}=\frac{y-y_1}{b}=\frac{z-z_1}{c}$

Now $(x_1,y_1,z_1)=(1,1,1),(a,b,c)=(0,1,0)$

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