No, you don't need parametric equations for the planes but you do need parametric equations for the line of intersection. The simplest way to do this is to solve the two equations. For example, subtracting the first equation from the second eliminates x given 4y- 5z= 10 or y= (5z+ 10)/2. Because there are only two equations you cannot solve for y or z separtely but you can put y= (5z+10)/2 back into either of the first equations and solve for x as a function of z. Then use z itself as parameter!megr_ftw said:Homework Statement
Find the vector equation for the line of intersection of the planes x + 4y - 2z = 5 and
x + 3z = -5
r= (__,__,0) + t(12,__,__)
Homework Equations
equation of a plane= a(x-x0)+b(y-y0)+c(z-z0)= 0
The Attempt at a Solution
Do I need to convert the equations of the planes into parametric equations?
Intersecting planes in 3-d space refer to two or more planes that share a common point or line. In other words, they intersect at a specific location in three-dimensional space.
If two planes are not parallel, they will intersect at a single point. This can be determined by setting the equations of the planes equal to each other and solving for the variables. If the resulting solution is a single point, then the planes intersect.
When three planes intersect in 3-d space, they will form a single point of intersection. This is because each plane can only intersect with the other two planes at a single point.
No, two planes cannot be parallel and intersect in 3-d space. If two planes are parallel, they will never intersect, no matter how far they are extended.
Some real-life examples of intersecting planes in 3-d space include the intersecting walls and ceiling of a room, the intersection of two roads on a map, and the intersection of two airplane flight paths in the sky.