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VectorsVocab - • Scalar – a quantity that has magnitude...

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Vocabulary: Vectors Vocabulary Component – the projection of a vector in a given direction. o On a coordinate grid, a vector can be described by an x component and a y component. o For example, the vector 3 i + 4 j has an x component of +3 and a y component of +4. Dot product – for vectors, the result of multiplying corresponding components and adding those products. o For example, the dot product of (3 i + 4 j ) and (5 i + 2 j ) is 15 + 8 = 23 o Dot products are scalar quantities, not vectors. o Dot products are used for various purposes in geometry, trigonometry, calculus, and physics. For example, dot products are used to calculate how much mechanical work is done. Work, a scalar quantity, is equal to the dot product of force and displacement, both vector quantities ( W = F • d ). Magnitude – the size, brightness, or intensity of an object or event. o The magnitude of a vector is its length. o The magnitude of a vector is written: || x ||. Resultant – a vector representing the sum of two or more vectors.
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Unformatted text preview: • Scalar – a quantity that has magnitude, but no direction. o Examples of scalars include speed, temperature, and volume. • Unit vector notation – a method of writing the components that make up a vector. o In unit vector notation, the i component represents displacement along the x-axis of a coordinate grid and the j component represents displacement along the y-axis. o For example, if a vector has an x component of +3 and a y component of +4, its unit vector notation would be 3 i + 4 j . • Vector – a representation that specifies the direction and magnitude of a quantity. o In physics, vectors are used to represent displacement, velocity, acceleration, force, and other quantities that have a specific direction. o Vectors are represented visually by arrows. o Vectors in equations are represented by bold letters such as d (displacement) and F (force)....
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VectorsVocab - • Scalar – a quantity that has magnitude...

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