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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

Luke Alvarez

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

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))#

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Answer 2

Emily Ammerman

The parametric equations of the line through the origin and parallel to the line determined by (x = 2t), (y = 1 - t), and (z = 4 + 3t) are:

[x = 2s] [y = 1 - s] [z = 4 + 3s]

where (s) is a parameter.

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Answer from HIX Tutor

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