Thread: Equation of plane from 2 lines

OK here is the question.

Find an equation of the plane that contains the lines given by

(x-1)/-2 = y = z+1

and

(x+1)/-2 = y-1 = z-2

This is what I did.

I found 2 points for the first line and 2 points for 2nd line

A= (0 , 0.5, -0.5)
B=(1 , 0 , 1)

C= (0, 0.5, 1.5)
D= (1, 0, 1)

then i got their vector equations
AB = <1, -0.5, 1.5>
CD = <1, -0.5, -0.5>

What now? Do i get their cross product? I did cross product, substituted it with a point on the plane, point A i think, and then got the equation x+2y = 1.

But the answer doesnt seem right to me, so I would like some clarification as to whether I did anything wrong.

Originally Posted by adamantine

OK here is the question.

Find an equation of the plane that contains the lines given by

(x-1)/-2 = y = z+1

and

(x+1)/-2 = y-1 = z-2

This is what I did.

I found 2 points for the first line and 2 points for 2nd line

A= (0 , 0.5, -0.5)
B=(1 , 0 , 1)

C= (0, 0.5, 1.5)
D= (1, 0, 1)

then i got their vector equations
AB = <1, -0.5, 1.5>
CD = <1, -0.5, -0.5>

What now? Do i get their cross product? I did cross product, substituted it with a point on the plane, point A i think, and then got the equation x+2y = 1.

But the answer doesnt seem right to me, so I would like some clarification as to whether I did anything wrong.

It looks fine to me: it's easy to check that contains both lines...

Tonio