Overview
This lesson introduces vectors, their definitions, types, geometric representations, direction notation, and relationships such as parallel, equivalent, and opposite vectors.
Scalars vs. Vectors
- A scalar is a quantity with magnitude only (e.g., temperature, distance, speed, mass).
- A vector is a quantity with both magnitude and direction (e.g., velocity, force).
Types and Representation of Vectors
- Geometric vectors are represented as directed line segments with specific magnitude (length) and direction (arrowhead).
- Notation for vectors uses two points and a right-pointing arrow above, e.g., (\vec{AB}).
- The starting point is called the tail; the end point is the tip or head.
- The magnitude of a vector is written with absolute value bars, e.g., (|\vec{AB}|), and is always non-negative.
Describing Vector Direction
- Directions can be described by the angle counterclockwise from a horizontal line.
- True bearings measure the angle clockwise from North, always with three digits (e.g., 060°).
- Quadrant bearings specify an angle (0°–90°) from North or South towards East or West (e.g., South 35° West).
Converting Between Bearings
- To convert true bearing (clockwise from North) to quadrant bearing, find the difference from 180° and specify direction.
- To convert quadrant bearing (e.g., North 50° West) to true bearing, subtract the angle from 360° for the clockwise measure from North.
Vector Relationships and Properties
- Parallel vectors have the same or exact opposite direction, regardless of magnitude.
- Equivalent vectors have the same magnitude and direction, regardless of position.
- Opposite vectors have the same magnitude but exactly opposite directions.
- The opposite of (\vec{AB}) can be written as (\vec{BA}) or (-\vec{AB}).
Key Terms & Definitions
- Scalar — a quantity with magnitude only.
- Vector — a quantity with both magnitude and direction.
- Magnitude — the length of a vector, always non-negative.
- True Bearing — angle measured clockwise from North, always written with three digits.
- Quadrant Bearing — direction given as an angle from North or South towards East or West, between 0° and 90°.
- Parallel Vectors — vectors with the same or opposite directions.
- Equivalent Vectors — vectors with equal magnitude and direction.
- Opposite Vectors — vectors with equal magnitude but opposite direction.
Action Items / Next Steps
- Practice drawing vectors and converting between true and quadrant bearings.
- Complete the assigned practice questions for this lesson.