The Cartesian equation of a line through (x 1 ,y 1 ,z 1 ) with direction ratios a,b,c is:

(x-x 1 )/a = (y-y 1 )/b = (z-z 1 )/c

x/a = y/b = z/c, without referencing the given point

ax + by + cz = 0, the plane equation form

x + y + z = constant, a single linear relation

📐 Mathematics · Three Dimensional Geometry · JEE

The Cartesian equation of a line through (x₁,y₁,z₁) with direction ratios a,b,c is:

Answer: (x-x₁)/a = (y-y₁)/b = (z-z₁)/c.

Correct answer: D. (x-x₁)/a = (y-y₁)/b = (z-z₁)/c

Explanation: Symmetric (Cartesian) form: (x-x₁)/a = (y-y₁)/b = (z-z₁)/c. Each fraction equals the parameter lambda.

Three mutually perpendicular axes x, y, z meeting at the origin O, with a point P located by its (x, y, z) coordinates.

Lines and planes in 3D space, direction cosines, distances, and angles