# PHYS50 - Introduction to Vectors

Many of the quantities that are part of our natural world are quantities that have both a magnitude and a direction associated with them. Examples are force, electric and magnetic fields, angular momentum, position, velocity, acceleration, to name a few. This course is an introduction to how vector quantities can be represented geometrically and algebraically, on concepts related to vectors and the spaces in which they exist, and on mathematical operations that can be performed on vector quantities.

This course is a prerequisite for all courses that pertain to vector quantities.

The course outline is as follows:

• Introduction
• Vectors vs Scalars
• Vectors as Geometric Objects
• Representation as Arrows
• Vector Magnitude
• The Multiplication of a Scalar and a Vector
• The Addition of Two Vectors
• The Subtraction of Two Vectors
• The Angle Between Two Vectors
• The Dot Product of Two Vectors
• The Span of a Set of Vectors
• Dimension
• The concept of basis
• Linear Independance
• Arbitrary Basis
• Orthogonal Basis
• Normal Basis
• Orthonormal Basis
• Cartesian Basis
• Vectors in One Dimension
• Vectors in Two Dimensions
• Vector Magnitude
• Multiplication of a Vector and a Scalar
• The Addition of Two Vectors
• The Subtraction of Two Vectors
• The Dot Product of Two Vectors
• Vectors in Three Dimensions
• Vector Magnitude
• The Addition of Two Vectors
• The Subtraction of Two Vectors
• The Dot Product of Two Vectors
• The Vector Cross Product
• Geometric Representation
• In Terms of Components
• The BAC-CAB Rule
• The Triple Scalar Product
• Vectors in Higher Dimensions
• Summary

This course does not assume any knowledge of calculus, but does assume that one has been introduced to basic algebra and trigonometry.

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