Vector Dot Product & Related Concepts

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Vocabulary flashcards covering formulas and terms hinted at in the notes, focusing on dot product, vector magnitude, cosine relationships, and work.

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8 Terms

1
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Cosθ = (A·B) / (|A||B|)

Formula that relates the cosine of the angle θ between two vectors A and B to their dot product and magnitudes.

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Dot Product (A·B)

A scalar obtained by multiplying corresponding components of two vectors and summing the results; used to find angles and calculate work.

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Vector Magnitude |A|

The length of a vector, calculated as the square root of the sum of the squares of its components.

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Work: W = F·d

The work done when a force F acts through a displacement d; equal to the dot product of force and displacement vectors.

7
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√50 (≈ 7.07)

Square root of 50; often appears when computing magnitudes such as |A| or |B|.

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Angle α (cos α)

The angle between two vectors (e.g., force and displacement); its cosine determines the component of one vector along the direction of the other.