Question

How do you write a vector equation and a parametric equation for each line: the line through A(3,0,4) and parallel to the x-axis?

Answer 1

`r=(3. 0, 4)+(x, 0, 0)=(x+3, 0, 4)` x can be regarded as the parameter for the parametric form.

Explanation:

Equation x-axis is`r= (x, 0, 0)`.

So, the equation to the line, parallel to the x-axis through (a, b, c) is

`r=(a, b, c)+(x, 0, 0)`.

Here, it is `r=(3, 0. 4)+(x, 0, 0)=(3+x, 0, 4)`.

This is itself in parametric form, with x as the parameter. Note that y

and z are constants on this line.