Physics

Vectors

Vectors

Introduction

• Vectors are fundamental in physics and represent quantities that have both magnitude (size) and direction.
• Unlike scalar quantities that have magnitude only, vectors require both a numerical value and a specified direction to fully describe them.

Examples of Vector Quantities

Vector quantities are used to describe various physical attributes, including:

• Displacement: The change in position of an object with both magnitude and direction, usually measured in meters (m).
• Velocity: The rate of change of displacement with respect to time, typically measured in meters per second (m/s) and including direction.
• Acceleration: The rate of change of velocity, often measured in meters per second squared (m/s²) and including direction.
• Force: A vector quantity representing a push or pull on an object, measured in newtons (N) and including direction.
• Weight: The force exerted on an object due to gravity, including both magnitude and direction.
• Momentum: A vector quantity representing an object's motion, calculated as the product of its mass and velocity, including direction.

Characteristics of Vector Quantities

Vectors possess the following characteristics:

• They require both magnitude and direction for a complete description.
• Vector quantities can be added or subtracted using vector algebra, considering both magnitude and direction.
• Changing either the magnitude or direction of a vector changes the vector itself.

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Vectors

Examples

Here are some examples of vector quantities:

• If you move 100 meters east, your displacement is a vector quantity because it includes both magnitude (100 m) and direction (east).
• A car travelling at a velocity of 60 km/h north is a vector quantity because it includes both the numerical value (60 km/h) and the direction (north).
• An object experiencing a force of 20 newtons to the right is described by a vector quantity, including both magnitude (20 N) and direction (right).
• When an aeroplane accelerates at 5 m/s² upwards, it represents a vector quantity with magnitude (5 m/s²) and direction (upwards).