A vector is a mathematical object that has both magnitude and direction, and is used to represent quantities such as force, velocity, and displacement in physics and engineering. Vectors are fundamental in linear algebra and are often represented as an ordered list of numbers, which can be manipulated using operations like addition, subtraction, and scalar multiplication.

Vector

mathematical object

Magnitude and direction are fundamental components of vectors, which are mathematical objects used to represent quantities that have both size and orientation in space. Understanding these components is essential for analyzing physical phenomena in fields such as physics and engineering, where vectors describe forces, velocities, and other directional quantities.

magnitude and direction

represent quantities

Force is a vector quantity that causes an object to undergo a change in speed, direction, or shape. It is described by Newton's laws of motion, which outline how forces interact with mass and acceleration.

force

Velocity is a vector quantity that describes the rate of change of an object's position with respect to time, including both speed and direction. It is fundamental in understanding motion and is essential in fields like physics and engineering for analyzing dynamic systems.

velocity

Displacement is a vector quantity that refers to the change in position of an object, defined as the shortest path between the initial and final points in a specific direction. It is distinct from distance, which measures the total path traveled regardless of direction, making displacement crucial for understanding motion in physics.

displacement

Physics is the fundamental science that seeks to understand the nature and behavior of matter and energy in the universe, covering phenomena from the smallest subatomic particles to the largest cosmic structures. It provides the foundational principles that underpin other sciences and technologies, offering insights into the laws governing the physical world and enabling advancements in various fields.

physics

Engineering is the application of scientific and mathematical principles to design, build, and analyze structures, machines, and systems, aiming to solve real-world problems efficiently and sustainably. It encompasses a wide range of specialized fields that address various aspects of technology and innovation, driving progress in industries and improving quality of life.

engineering

fundamental in linear algebra

ordered list of numbers

manipulated using operations

Addition is a fundamental arithmetic operation that combines two or more numbers to yield a sum, serving as the basis for more complex mathematical concepts. It is commutative and associative, allowing for flexible manipulation and calculation in various mathematical contexts.

addition

Subtraction is a fundamental arithmetic operation that involves finding the difference between two numbers, typically by removing the value of one number from another. It is essential for understanding concepts of negative numbers, inverse operations, and is widely used in various real-world applications such as calculating change, measuring differences, and solving equations.

subtraction

Scalar multiplication involves multiplying a vector by a scalar, resulting in a new vector that is scaled in magnitude but retains the same direction unless the scalar is negative, which reverses the direction. This operation is fundamental in linear algebra and is used to scale vectors in various applications, such as physics and computer graphics.

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