Calculus

Finding the intersection of 2 planes

If you have two planes, they can either be parallel, co-incident, or intersect on a line. I'll ignore the first two, and concentrate on finding the equation of the line of intersection.

Consider the planes − 2 x + 3 y + z + 6 = 0 and 3 x − y + 2 z − 2 = 0. If this was 2 lines is 2-space we would just use substitution or elimination to find a point (this is what you would do to intersect 3 planes, btw). Unfortunately, we have more variables than equations.

Heretofore, you have been dealing with scalar quantities. These are things like numbers, mass, length, that just have a size (magnitude). We will now formally introduce the vector. A vector is a mathematical object that has both a magnitude and a direction. Vectors are used to describe things like position, forces, weight, and hence play a big part in physics. In order to describe the direction of a vector, we need a frame of reference.

Rate of Change

Derivatives and their Applications

Implicit Differentiation