Question

How do you find the parametric equations of each line in space the line that intersects (4,5,-2) and is parallel to the z-axis?

Answer 1

`vec r(t) = ((4),(5),(-2)) + t ((0),(0),(1))`

Explanation:

any line that is parallel to the z axis has direction `\vec d = hat z = ((0),(0),(1))`

so the line that passes (4,5,-2) and is parallel to the z axis can be described most simply as

`vec r(t) = ((4),(5),(-2)) + t ((0),(0),(1))`