Question

How do you find the parametric equations of line through the origin and parallel to the line determined by x = 2t, y = 1 - t, z = 4 + 3t?

Answer 1

`mathbf r = t ((2), (- 1), (3))`

Explanation:

The line is:

`mathbf r = ((2t), (1 - t), (4 + 3t)) = ((0), (1 ), (4 )) + t ((2), (- 1), (3))`

And so has direction vector:

`mathbf d = ((2), (- 1), (3))`.

The line through the Origin with this direction can be written as:

`mathbf r = mathbf 0 + t mathbf d = t ((2), (- 1), (3))`