## Week 16

16.T Three-dimensional (3D) vectors and the cross product; applied max/min problems I

Reference: Stewart 11.2, 11.4, 3.8

Keywords: 3D vectors, determinant, cross product, right-hand rule, scalar triple product, optimization, applied max/min problems

Learning Objectives: The student will be able to:

• Use the bracket notation and the i, j, k notation for 3D vectors
• Perform basic arithmetic and algebraic computations with 3D vectors
• Represent a 3D vector graphically in a 3D rectangular coordinate system
• Compute the cross product of two 3D vectors
• Evaluate determinants of orders 2 and 3
• Evaluate the scalar triple product of three 3D vectors, and explain its geometrical interpretation
• Implement the steps in solving applied maximum and minimum problems:
• Read and understand the problem.
• Draw a diagram when appropriate; introduce notation.
• Use constraints to eliminate extra variables.
• Use calculus to find absolute maximum or minimum value of quantity to be optimized.

Reference: Stewart 3.8

Keywords: Optimization, applied max/min problems

Learning Objectives: The student will be able to:

• Solve applied maximum and minimum problems