## Vectors - 3D Analytic Geometry

Locations: Online, Los Gatos, Menlo Park

Cost: \$100/hr – \$130/hr

Recommended hours: 9-18

Goals:

• Learn about vectors and 3D geometry
• Answer interesting applied geometry problems using vectors
• Visualize and construct parametric vector functions to describe real world motion
• Visualize and interpret scalar and vector functions of vectors by constructing topographies and vector fields

## Course Description:

Most high school courses focus on two-dimensional geometry, leaving students mystified by the three-dimensional world around them. Fortunately, it’s relatively easy to generalize geometry and algebra to higher dimensions using vectors!

In this course, students will explore the geometry and algebra of vectors in both two and three dimensions. Students will learn to find the equations of curves, planes, and their possible intersections, and to parameterize them in useful ways. Students will soon be able to answer interesting questions like “What are the bond angles in a molecule?” and “How much leather does it take to make a soccer ball?”

Building upon vectors, interested students can explore relevant and related applications of matrix algebra. With these tools and insights, students can make conclusions and interpret possibilities of 3D space in practical and concise ways.

Students familiar with calculus can also explore more advanced topics, such as derivatives and applications of vector valued functions, directional derivatives of scalar functions, multiple integrals, path and surface integrals, gradient vectors, divergence, curl and Green’s theorem, and Gauss’s law. Knowledge of Calculus is not required for this course, although we recommend students have completed coursework in Algebra 2 Trigonometry or Precalculus.

## Make the Most of the Summer!

Students who stay actively engaged in the learning process during the summer perform better during the school year.

Peninsula Main Phone Number (650) 331-3251