Vectors

Front

Vector Noun

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[vek-ter]

Back

Vector

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A quantity that possesses both magnitude and direction, often visually represented by an arrow with a specific length.

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Example: This diagram shows forces as vectors acting on an object. Each arrow is a vector, indicating both the direction of the force and its magnitude (strength) by its length.

Front

Magnitude Noun

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[mag-ni-tood]

Back

Magnitude

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The size, length, or amount of a vector quantity, which is always expressed as a positive scalar value.

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Example: This diagram shows a vector, which is an arrow with a specific length and direction. The magnitude is the length or size of the arrow.

Front

Resultant Vector Noun

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[ri-zuhl-tnt vek-ter]

Back

Resultant Vector

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The vector sum of two or more individual vectors, representing the overall or combined effect of those vectors.

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Example: This image shows two forces (F1, F2) acting on an object being added together to create a single, equivalent force called the resultant vector (FR).

Front

Displacement Noun

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[dis-pleys-muhnt]

Back

Displacement

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A vector quantity that refers to an object's overall change in position from its starting point to its endpoint.

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Example: This diagram shows a person moving from an initial position (x₀) to a final position (x_f), illustrating displacement as the straight-line change in position.

Front

Pythagorean Theorem Noun

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[pi-thag-uh-ree-uhn thee-er-uhm]

Back

Pythagorean Theorem

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A mathematical formula used to find the magnitude of the resultant of two vectors at a right angle.

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Example: This image shows a right-angled triangle with side lengths a and b, and demonstrates how to calculate the length of the hypotenuse (c) using the Pythagorean theorem, a² + b² = c².

Front

Law of Cosines Noun

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[law uv koh-sahyns]

Back

Law of Cosines

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A trigonometric formula used to find a resultant vector's magnitude when component vectors are not at a right angle.

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Example: This diagram shows a triangle with labeled sides (a, b, c) and angles (α, β, γ), the standard setup for applying the Law of Cosines.

Front

Coordinate System Noun

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[koh-awr-dn-it sis-tuhm]

Back

Coordinate System

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A system using axes, like x and y, to uniquely determine the position and orientation of points or vectors.

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Example: This image shows a coordinate system, which uses a horizontal x-axis and a vertical y-axis to define the exact location of a point on a plane.

Front

Component Vectors Noun

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[kuhm-poh-nuhnt vek-terz]

Back

Component Vectors

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The projections of a single vector that are parallel to the x-axis and y-axis of a coordinate system.

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Example: This diagram shows a vector (the blue arrow) on a grid. Its component vectors are the separate horizontal ("2 units right") and vertical ("6 units up") movements that combine to create the main vector's path.

Front

Vector Resolution Noun

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[vek-ter rez-uh-loo-shuhn]

Back

Vector Resolution

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The process of breaking down a single vector into its individual horizontal (x) and vertical (y) components.

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Example: This diagram shows that a single vector ('Vector r') can be broken down, or resolved, into two separate parts: a horizontal component (Rh) and a vertical component (Rv).

Front

Quadrant Noun

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[kwod-ruhnt]

Back

Quadrant

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One of the four regions into which a plane is divided by the horizontal x-axis and vertical y-axis.

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Example: A coordinate plane is divided by the x-axis and y-axis into four sections called quadrants, each with a specific sign pattern for coordinates.