Lines and Planes
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Intersection of two planes
If two distinct planes in \(\mathbb{R}^3\) are not parallel, they intersect, and the intersection forms a line. A natural question is to find an equation of that line.
For an equation of a line, we need a point on the line and its direction vector. Since the line lies in both of the planes, its direction vector must be orthogonal to both of the normal vectors. Let’s look at few examples:
Couple of examples
Try it yourself
Intersection of a line and a plane
If a line is not parallel to a plane, it will intersect it at a single point. Finding this point is simple: we just need to find the time at which the coordinates of a moving object described by the parametric equations of the line satisfy the equation of the plane: