   Chapter 12, Problem 13RCC

Chapter
Section
Textbook Problem

# Write a vector equation, parametric equations, and symmetric equations for a line.

To determine

To write: A vector equation for a line.

Explanation

Consider a line that passes through a point with position vector r0 and it is parallel to a vector v.

The vector equation for a line is written as follows.

r=r0+tv

Here,

r0 is the position vector,

t is the scalar parameter, and

v is the vector which is parallel to the line.

Thus, the vector equation for a line is r=r0+tv_.

To write: The parametric equations for a line.

Solution:

The parametric equations for a line are x=x0+at,y=y0+bt,z=z0+ct_.

Consider a line that passes through a point P(x0,y0,z0) and it is parallel to a direction vector v=a,b,c.

The parametric equations for a line are written as follows.

x=x0+at,y=y0+bt,z=z0+ct

Here,

(x0,y0,z0) is a point through which the line passes and

a, b, and c are the direction numbers of direction vector v

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