Question

Find a vector parametrization r(t) for the line with the given description. Passes through P = (5, 0, 3), direction vector v = 3, 0, 5

Answer 1

Explanation:

Given that a line passes through a point

P = (5, 0, 3)

Direction vector =
`v = 3, 0, 5`

Let (x,y,z) =r(t) be any general point on the line

We have

`x-5, y-0, z-3` will be proportional to v

Or
`(x-5)/(3) =(y)/(0) =(z-3)/(5)`

Let this equals t

Then parametric form

=
`r(t) = (5+3t)i +0.j+(3+5t)k`