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

Answer:

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

Step-by-step 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

$\frac{x-3}{0} =\frac{y-2}{-4}=\frac{z-1}{2}=t$

Here t is the parameter

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

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