Chapter Review

This chapter developed vector algebra from the ground up: what a vector is and how it differs from a scalar; how to add, subtract, and scale vectors both geometrically (triangle/parallelogram laws) and algebraically (component-wise); how position vectors turn point-geometry problems — midpoints, section ratios, collinearity, concurrency of medians — into vector computations; how to resolve any vector into its rectangular components along coordinate axes, and read off its direction cosines and direction ratios; and finally, the two products of two vectors — the scalar (dot) product, which measures projection and tests perpendicularity, and the vector (cross) product, which returns a vector perpendicular to both factors and whose magnitude is a parallelogram's area, and which tests parallelism. …