Yes, you can use PQ×QR or, for that matter, PR×QR . Each gives a vector which is normal to the plane.Calpalned said: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 said: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.
A scalar equation of a plane is a linear equation that represents a plane in three-dimensional space. It is in the form of ax + by + cz + d = 0, where a, b, and c are the coefficients of the variables x, y, and z, and d is a constant.
A scalar equation of a plane only uses linear combinations of the variables x, y, and z, while a vector equation uses the cross product of two vectors to represent the plane. A scalar equation is also simpler and easier to work with in most cases.
A scalar equation of a plane is determined by finding the normal vector of the plane, which is a vector perpendicular to the plane, and using it to form the equation ax + by + cz + d = 0. The coefficients a, b, and c can be determined by using the coordinates of three points on the plane.
Yes, a scalar equation of a plane can be used to graph the plane by solving for one of the variables and treating the other two variables as parameters. This will result in a linear equation in two variables, which can be graphed on a two-dimensional coordinate plane.
Yes, there are special cases when finding the scalar equation of a plane. For example, if the plane is parallel to one of the coordinate axes, the corresponding coefficient in the equation will be zero. Also, if the plane passes through the origin, the constant term d will be zero.