Proving associative and scalar multiplication properties for vectors

Using vectors to prove the midpoint formula and a fact about quadrilaterals

Using vectors to prove facts about equilateral triangles and a scalar multiplication property for the dot product

Proofs of the Cauchy-Schwarz Inequality and a property of vector projections

Proving the Triangle Inequality and a property of the midpoints of rectangles

Proving a certain parameterization gives the unit circle and showing vector equations of lines are parallel

Proving facts about the derivatives of vector functions including the product rule

Calculating slopes of tangent lines to parametric curves

Using the limit definition to find derivatives of functions and vector functions