How to derive the equation for the distance between two points using the Pythagorean Theorem.
How to derive the formula for the midpoint of a segment in three dimensions.
How to derive the distance formula for polar coordinates.
How to predict the direction of a vector.
How to express velocity as a vector.
Understanding the components of vectors.
How to express a vector algebraically in terms of the unit vectors i and j.
Understanding the differences between empirical and molecular formulas.
How to find a vector normal (perpendicular) to a plane given an equation for the plane.
How to derive the cosine of a difference formula.
How to write the vector equation of a line.
How to derive the equation for a circle using the distance formula.
How to compute the sum of two vectors or the product of a scalar and a vector.
How to compute the angle between two vectors.
How to use the sine and cosine addition formulas to prove the double-angle formulas.
How to add vectors geometrically two ways.