Vector Addition

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Vector Noun

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[vek-ter]

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Vector

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A physical quantity that is defined by possessing both a specific magnitude (size) and a particular direction in space.

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Example: This image shows two forces (vectors) pulling a box in the same direction. The diagram shows how these force vectors, F1 and F2, add together to create a larger resultant force, FR.

Front

Scalar Quantity Noun

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[skay-ler kwon-ti-tee]

Back

Scalar Quantity

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A physical quantity that is fully described by its magnitude or numerical value alone, without any associated direction.

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Example: Using the formula F=ma, this image shows that mass (m) is a scalar quantity, meaning it only has magnitude (like 5 kg).

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 a positive scalar value independent of direction.

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Example: This diagram shows a vector, which has both size and direction. The length of the arrow represents its magnitude (how big it is).

Front

Direction Noun

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[di-rek-shun]

Back

Direction

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The orientation of a vector in space, indicating the path along which it is aligned or pointing.

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Example: A compass illustrates direction using cardinal points (N, S, E, W) and degrees. Direction is a crucial component of a vector, specifying its orientation.

Front

Displacement Noun

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[dis-pleys-muhnt]

Back

Displacement

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A vector quantity representing the shortest distance and direction from an object's initial position to its final position.

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Example: A person moves from an initial position (1.5 m) to a final position (3.5 m), resulting in a displacement of +2.0 meters.

Front

Distance Noun

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[dis-tuhns]

Back

Distance

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A scalar quantity that represents the total path length an object has traveled, regardless of its starting or ending point.

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Example: This diagram shows that distance is the total length of the path traveled (the winding 8 km road), not the straight-line path between start and end.

Front

Vector Components Noun

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[vek-ter kom-poh-nents]

Back

Vector Components

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The projections of a vector onto a set of axes, typically perpendicular, that sum together to form the original vector.

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Example: This diagram shows how a single vector (blue arrow) can be split into its horizontal and vertical parts, called components (red arrows).

Front

Resultant Vector Noun

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[ri-zuhl-tuhnt vek-ter]

Back

Resultant Vector

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The single vector that represents the combined effect or sum of two or more individual vectors acting together.

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Example: Adding vector 'a' and vector 'b' head-to-tail results in the red 'resultant vector' (a+b), which shows the total displacement from start to finish.

Front

Pythagorean Theorem Noun

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[pi-thag-uh-ree-uhn thee-uh-ruhm]

Back

Pythagorean Theorem

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A mathematical formula (a² + b² = c²) relating the sides of a right triangle, used to find a resultant's magnitude.

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Example: This diagram shows a right-angled triangle, labeling the two shorter sides as 'legs' (a, b) and the longest side as the 'hypotenuse' (c).

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Perpendicular Adjective

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[pur-puhn-dik-yuh-ler]

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Perpendicular

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Describes two lines, planes, or vectors that intersect or meet at a right angle of exactly 90 degrees.

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Example: This diagram shows two lines intersecting at a 90-degree angle, which is the definition of perpendicular. The arrows suggest these could be vectors.