Vector Essentials for Calc 3, Algebra - Calculus 3

This video covers essential vector topics for Calculus 3, including vectors vs scalars and basic notation, position vectors, vector components and magnitude, vector addition and scalar multiplication, properties of vector operations, subtraction, unit vectors and normalization, dot product, orthogonality, angle between vectors and projection, vector cross product, determinant form and properties, scalar triple product and determinant form, and worked examples.

0:00 Vectors vs scalars, basic notation
2:11 Position vectors, vector components and magnitude
5:41 Vector addition and scalar multiplication
9:45 Properties of vector operations
12:50 Vector subtraction
15:03 Unit vectors, normalizing vectors
17:37 Dot product, orthogonality
20:39 Properties of the dot product
22:27 Vector projection
25:20 Vector cross product
29:09 Determinant form of the cross product
31:32 Properties of the cross product
34:32 Scalar triple product
37:26 Determinant form of the scalar triple product
39:00 Worked examples