Question

Find the parametric equations for the line that passes through the point P (3,2,1) and is parallel to the vector v = (0,-4,2)

Answer 1

`(x,y,z) = (3, 2-4t, 1+2t)`

Explanation:

Given that a straight line passes through the point P(3,2,1)

Also given that the line is parallel to vector V = (0,-4,2)

This implies that the required line has direction ratios as (0,-4,2)

Hence in cartesian form we can represent the line as

`(x-3)/(0) =(y-2)/(-4)=(z-1)/(2)=t`

Here t is the parameter

In other words, any point on the line is represented parametrically as

`(x,y,z) = (3, 2-4t, 1+2t)`