Test 1

Can use...

• calculator
• one 8 1/2 X 11 page of notes that you prepare ahead of time.

Can't use...

• Interwebs, or textbook,
• CoCalc / GeoGebra / Mathematica,
• Each other

Topics

From Chapter 9, Sections 1-6

• Plot points in 3D space.
• Draw coordinate axes from different viewpoints.
• Geometrically determine sums and differences of vectors, scalar products of vectors, projections of vectors onto other vectors, find components of vectors.
• Determine sums and differences of vectors in component form.
• Find distances between points.
• Find lengths of vectors.
• Know the difference between points and vectors.
• Compute dot and cross products.
• Know relationship between dot and cross products and the angles between vectors.
• Apply dot and cross products - areas of parallelograms, volumes of parallelpipeds, angles between vectors, force and work or torque.
• Equations of lines (parametric, vector equation, symmetric equations).
• Equations of planes (normal to a plane, standard form, parametric functions).
• Rectangular, Cylindrical, Spherical coordinate systems and converting between them.
• Identifying surfaces in space given equations for such surfaces; Horizontal / vertical traces.

Topics from Chapter 10, Sections 1-4.

• Vector functions, parametric curves.
• Curves in space and sketching curves in space; Projections of a curve.
• Derivatives of a vector valued function.
• Tangent line to a space curve. Unit tangent vector.
• Arc length.
• Curvature.
• Relationship between vector valued function (position vector), the derivative (velocity vector), the second derivative (acceleration vector).
• Tangential and normal components of acceleration.