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Think in terms of magnitude (which can be positive or negative) and direction. Think of a scalar. It has a magnitude but it doesn't have a direction. It's 0-dimensional. Think of a vector. It has a magnitude (the size of the vector) and it also has a direction, which points in a straight line through the origin. It's 1-dimensional. For example, the vector (2,0,0) has magnitude 2 and points along the X-axis. You could write that as 2 * x, if x is the vector (1,0,0). A bivector also has a magnitude, but instead of being 0-dimensional (like a scalar) or 1-dimensional (like a vector, it's 2-dimensional. So you could have a bivector that "points" along the entire XY-plane (remember: two-dimensional) and has some magnitude, say, 5. You could write that as 5 * x * y, if x is (1,0,0) and y is (0,1,0). If you attach physical units to these things, then you might have units of meters for vectors, and square meters for bivectors. Having an understanding of subspaces in linear algebra is helpful. |