Question

Do the parametric equations `x = 3t^3 + 7`, `y = 2 - t^3`, `z = 5t^3 + 1` determine a line?

Answer 1

yes

Explanation:

well, you can see that

`[x,y,z]^T = [7,2,1]^T + t^3 [3,-1,5]^T`

if we replace `t^3` with `lambda` , which we are perfectly entitled to do, we see that this is the more recognisable equation of a straight line in `\mathbf{R}^3`:

`[x,y,z]^T = [7,2,1]^T + lambda [3,-1,5]^T`