Definition: Vector and position vector;
Definition: Equality of vectors;
Definition: Addition of vectors;
Definition: Multiplication of a vector by a scalar;
Definition: the unit vectors i and j.
Rectangular coordinates;
Distance formula.
Dot product, properties of the dot product;
Interpretation of the dot product;
Test for perpendicular vectors;
Direction angles and projections.
Examples.
Section 12.3 Topics:
Vector product;
Theorem 1: Perpendicularity
of the cross product;
Theorem 2: Length of the
cross product;
Theorem 3: Algebraic
properties
of the cross product;
Theorem 4: Scalar triple
products and volume;
Geometric
significance of
the cross product;
Parallel vectors;
Section 12.4 Topics:
Line in space;
Vector equation of a line;
Parametric equation of
a line;
Symmetric equation of
a line;
Plane in space;
Vector equation of a plane;
Scalar equation of a plane;
Angle between given planes;
Examples.