How to convert cartesian to parametric ( VECTOR, PLANES)

• Sep 1st 2008, 03:04 AM
wonderrrgirl
How to convert cartesian to parametric ( VECTOR, PLANES)
Hi, I need some help with this question.

The plane 3x-2y+z=7 contains the point (1,-2,0) and is perpendicular to (3,-2,1).

find the equation of the plane in parametric form.

thanks!
• Sep 1st 2008, 03:10 AM
mr fantastic
Quote:

Originally Posted by wonderrrgirl
Hi, I need some help with this question.

The plane 3x-2y+z=7 contains the point (1,-2,0) and is perpendicular to (3,-2,1).

find the equation of the plane in parametric form.

thanks!

"The plane ..... contains the point (1,-2,0) and is perpendicular to (3,-2,1)" is redundant information since this information is contained in the given Cartesian equation.

Let x = t and y = s. Then z = 7 - 3x + 2y = 7 - 3t + 2s.

This is one of an infinite number of possible parametric forms.
• Sep 1st 2008, 03:17 AM
wonderrrgirl
So there can be more than one answer?
Thanks!
• Sep 1st 2008, 03:21 AM
mr fantastic
Quote:

Originally Posted by wonderrrgirl
So there can be more than one answer?
Thanks!

Yes.

Another possible answer is x = t + 1, y = s + 1, z = 7 - 3x + 2y = 7 - 3(t+1) + 2(s+1) = 6 - 3t + 2s.