Equation of a Line Through a point and
in the Direction of a Vector in 3 D

A calculator and solver that finds the equation of a line through a point and in a given direction in 3D is presented. The equation is written in vector, parametric and symmetric forms. As many examples as needed may be generated along with all the detailed steps needed to answer the question.

Below is shown a line through point \( P(x_p,y_p,z_p) \) and in the same direction as vector \( \vec v = \lt x_v,y_v,z_v \gt \).

Line through a point and parallel to a vector

Three forms of the equation of the line:

equations of Line through a point and parallel to a vector







Step by step solution

STEP 1: Vector form.

STEP 2: Parametric form.

STEP 3: Symmetric form.

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