stanford1463 said:bump...can anyone please see if I am right or wrong??
stanford1463 said:Homework Statement
Find the equation of the plane through vectors u=(1,1,2) parallel to the plane containing v=(2,2,-1), w=(1,-1,0), and the origin.
Homework Equations
The Attempt at a Solution
I did the cross product of v x w = (-1,-1,-4).
Thus, my equation became -x-y-4z=-9. Is this correct? Thanks.
The equation of a 3-dimensional plane is a mathematical representation of a flat surface in three-dimensional space. It is typically written 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 term.
A 3-dimensional plane has three variables (x, y, and z) and therefore requires three equations to represent it, while a 2-dimensional plane only has two variables (x and y) and requires two equations. Additionally, a 3-dimensional plane exists in three-dimensional space, while a 2-dimensional plane exists in two-dimensional space.
The equation of a 3-dimensional plane gives us information about the position and orientation of the plane in three-dimensional space. It can also be used to determine the distance between a point and the plane, and to find the intersection of two planes.
To graph a 3-dimensional plane, we can plot three points that satisfy the equation and connect them to form a triangle. This triangle represents the plane in three-dimensional space. Alternatively, we can use a computer program or graphing calculator to plot the plane.
Yes, the equation of a 3-dimensional plane can also be written in the form of vector equations, parametric equations, or as the intersection of two linear equations. However, the standard form (Ax + By + Cz + D = 0) is the most commonly used and easiest to work with.