Question

A line passes through \[A(x_1,y_1,z_1)\] and has direction ratios \[a,b,c\]. Which is its Cartesian equation?

पर्याय

• \[\frac{x+x_1}{a}=\frac{y+y_1}{b}=\frac{z+z_1}{c}\]

• \[\frac{x-x_1}{a}=\frac{y-y_1}{b}=\frac{z-z_1}{c}\]

• \[\frac{x-x_1}{x}=\frac{y-y_1}{y}=\frac{z-z_1}{z}\]

• \[\frac{x-a}{x_1}=\frac{y-b}{y_1}=\frac{z-c}{z_1}\]

Answer 1

The Cartesian form uses the coordinates \[x_1,y_1,z_1\] of a point on the line. Its denominators are the corresponding direction ratios \[a,b,c\].