You might be able to do it this way, but it's sort of the long way around. The cross product will give you a vector in the direction of the intersecting line, but you'll still need to find a point that is on the line.Loppyfoot said:Homework Statement
The planes 3y-4x-4z = -18 and 3x-2y+3z = 14 are not parallel, so they must intersect along a line that is common to both of them. The vector parametric equation for this line is: L(t)= ?
Homework Equations
Cross Product Seems like it would be relevant here, but how would I find the intersection point to plug into the result of the cross product?
A vector plane problem involves finding the intersection point or line between two or more planes in three-dimensional space using vector equations.
To find the parametric equations of an intersection line, you first need to find the direction vector of the line. This can be done by taking the cross product of the normal vectors of the two intersecting planes. Then, choose a point on the line and use the direction vector to create the parametric equations.
You need the equations of the planes involved and the methods for finding the intersection point or line, such as the cross product method or the Gaussian elimination method.
Yes, there are special cases where the planes may be parallel or coincident, resulting in no intersection or infinite solutions. These cases require special consideration and may not have a unique solution.
Vector plane problems can be solved by hand using basic algebra and vector operations. However, for more complex problems or multiple planes, software such as MATLAB or Wolfram Alpha may be helpful for faster and more accurate solutions.