Finding the scalar equation of a plane

[Calpalned]

Homework Statement

Find the equation of the plane that goes through points P, Q and R. P = (3, -1, 2), Q = (8, 2, 4) and R = (-1, -2, -3)

Homework Equations

Eq of plane
0 = a(x - x₀) + b(y - y₀) + c(z - z₀)

The Attempt at a Solution

In order to find vector normal to the plane, my teacher took the cross product of PQ X PR. Would I still get the correct normal vector if I take the cross product of PQ X QR? Finally, when I plug in the numbers to the equation in "

Homework Equations

", does it matter which point I choose (P, Q or R) for x₀, y₀, or z₀? Thank you.

 

[SammyS]

Homework Statement

Find the equation of the plane that goes through points P, Q and R. P = (3, -1, 2), Q = (8, 2, 4) and R = (-1, -2, -3)

Homework Equations

Eq of plane
0 = a(x - x₀) + b(y - y₀) + c(z - z₀)

The Attempt at a Solution

In order to find vector normal to the plane, my teacher took the cross product of PQ X PR. Would I still get the correct normal vector if I take the cross product of PQ X QR? Finally, when I plug in the numbers to the equation in "

Homework Equations

", does it matter which point I choose (P, Q or R) for x₀, y₀, or z₀? Thank you.

Yes, you can use PQ×QR or, for that matter, PR×QR . Each gives a vector which is normal to the plane.

No, it doesn't matter which point you use. Try more than one and compare results.

 

[Calpalned]

Yes, you can use PQ×QR or, for that matter, PR×QR . Each gives a vector which is normal to the plane.

No, it doesn't matter which point you use. Try more than one and compare results.

Thank you