shamus390 said: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
shamus390 said: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 agree with Dick that ∏(A, B, C) is just notation that identifies a plane.Dick said: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 said: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."
shamus390 said:Ah, dropped the negative sign, is x-y=-1 correct?
Multiplying an equation of a plane by a constant means to multiply every term in the equation by that constant. This will result in a new equation with the same form as the original, but with all coefficients and constant terms multiplied by the constant.
Multiplying an equation of a plane by a constant can help simplify the equation or make it easier to solve for certain variables. It can also be used to scale the equation to fit specific requirements or to find multiple solutions.
Multiplying the equation of a plane by a constant will result in a graph that is parallel to the original plane, but may be shifted or scaled depending on the value of the constant. The overall shape and orientation of the plane will remain the same.
Yes, you can divide an equation of a plane by a constant, as long as the constant is not equal to zero. This will result in a new equation with the same form as the original, but with all coefficients and constant terms divided by the constant.
Yes, you can multiply an equation of a plane by a negative constant. This will result in a new equation with the same form as the original, but with all coefficients and constant terms multiplied by the negative constant. This will change the orientation of the plane, as it will be reflected across the origin.