Equation of a plane multipled by a constant.

[shamus390]

Homework Statement

Given the points A(1,2,3) B(0,1,2) and C(2,3,-1) find:
a.) a vector perpendicular to the plane pi(A,B,C)
b.) the equation of the plane pi(A,B,C)

The Attempt at a Solution

a.) ∏<5,-5,0>
b.)∏(x-y)=∏

Am I incorrect in assuming that I would find the normal vector and plane equations as normal and multiply the result by Pi? The question seems counter-intuitive to me because couldn't Pi be factored out at anytime?

Thanks in advance

 

[LCKurtz]

Homework Statement

Given the points A(1,2,3) B(0,1,2) and C(2,3,-1) find:
a.) a vector perpendicular to the plane pi(A,B,C)
b.) the equation of the plane pi(A,B,C)

The Attempt at a Solution

a.) ∏<5,-5,0>
b.)∏(x-y)=∏

Am I incorrect in assuming that I would find the normal vector and plane equations as normal and multiply the result by Pi? The question seems counter-intuitive to me because couldn't Pi be factored out at anytime?

Thanks in advance

I have never seen the notation Pi(A,B,C) for a plane. What does that mean? Do you mean the equation of the plane passing through the given three points? If so, $\pi$ doesn't have anything to do with it.

 

[Dick]

Homework Statement

Given the points A(1,2,3) B(0,1,2) and C(2,3,-1) find:
a.) a vector perpendicular to the plane pi(A,B,C)
b.) the equation of the plane pi(A,B,C)

The Attempt at a Solution

a.) ∏<5,-5,0>
b.)∏(x-y)=∏

Am I incorrect in assuming that I would find the normal vector and plane equations as normal and multiply the result by Pi? The question seems counter-intuitive to me because couldn't Pi be factored out at anytime?

Thanks in advance

I think the question is just using the notation 'pi(A,B,C)' to mean the plane through the points A, B and C. I don't think it's supposed to be the number pi.

 

[Mark44]

I think the question is just using the notation 'pi(A,B,C)' to mean the plane through the points A, B and C. I don't think it's supposed to be the number pi.

I agree with Dick that ∏(A, B, C) is just notation that identifies a plane.

 

[shamus390]

So essentially he is using ∏ to name the plane? Either I'm misunderstanding or this was a strange question (its from a review sheet for an exam Thursday).

 

[Mark44]

That's what Dick and I think. Instead of identifying it as P(A, B, C), the instructor used the equivalent Greek letter to (possibly) prevent you from thinking the P stood for "point."

 

[Dick]

That's what Dick and I think. Instead of identifying it as P(A, B, C), the instructor used the equivalent Greek letter to (possibly) prevent you from thinking the P stood for "point."

And the equation of your plane isn't quite correct in any event.

 

[shamus390]

Ah, dropped the negative sign, is x-y=-1 correct?

 

[Dick]

Ah, dropped the negative sign, is x-y=-1 correct?

Yep.

 

[shamus390]

Thanks to both of you.