Vectors

Front

Vector Noun

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[vek-ter]

Back

Vector

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A quantity that has both magnitude and direction, used to represent physical quantities like force or displacement.

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Example: The arrow represents a vector, showing both the direction of the push (a force) and indicating it has a certain strength (magnitude).

Front

Resultant Vector Noun

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[ri-zuhl-tnt vek-ter]

Back

Resultant Vector

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The single vector that is the sum of two or more vectors, representing their combined effect on an object.

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

Front

Magnitude Noun

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[mag-ni-tood]

Back

Magnitude

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The size, length, or amount of a vector, which is always a positive scalar quantity indicating 'how much'.

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Example: A speedometer shows the magnitude of a car's speed, which is the amount or size of its speed, like 295 kilometers per hour.

Front

Direction Noun

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[di-rek-shun]

Back

Direction

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The orientation of a vector in space, typically defined by an angle measured from a reference axis.

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Example: The arrows on the road and the traffic sign show that cars move in specific, opposite directions.

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 end point.

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Example: This icon shows an object moving down a ramp, representing a change in its position, which is the basic idea of displacement.

Front

Components Noun

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[kuhm-poh-nuhnts]

Back

Components

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The projections of a single vector onto the perpendicular axes of a coordinate system, typically the x and y axes.

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Example: A wave is made of several components, such as its highest point (crest), lowest point (trough), height (amplitude), and length.

Front

Vector Resolution Noun

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

Back

Vector Resolution

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The process of breaking down a single vector into its individual perpendicular components, such as its x-component and y-component.

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Example: This diagram shows a force vector (purple arrow) being broken down, or resolved, into its separate vertical and horizontal parts (components).

Front

Pythagorean Theorem Noun

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

Back

Pythagorean Theorem

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A formula (R² = A² + B²) used to calculate the resultant's magnitude when adding two vectors at a right angle.

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Example: In a right-angled triangle, the square of the hypotenuse (side c) is equal to the sum of the squares of the other two sides (a and b).

Front

Law of Cosines Noun

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[law ov koh-sahyns]

Back

Law of Cosines

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A formula used to find a resultant vector's magnitude when the angle between two added vectors is not 90°.

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Example: This image shows the Law of Cosines formula and a labeled triangle, relating a side's length to the other two sides and their included angle.

Front

Coordinate System Noun

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

Back

Coordinate System

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A system with an origin and perpendicular axes used to describe the position and direction of vectors in space.

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Example: This image shows a coordinate system with a horizontal x-axis and a vertical y-axis that intersect at the origin (0,0).