Dot Product definitions Flashcards
Dot Product definitions
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Dot Product An operation combining two vectors by multiplying like components and summing, resulting in a scalar indicating their alignment. Scalar A single numerical value, often the result of a dot product, representing magnitude without direction. Vector A quantity with both magnitude and direction, often represented in component form such as i and j. Component A part of a vector along a specific axis, such as the x or y value in a two-dimensional vector. Alignment The degree to which two vectors point in the same or opposite directions, indicated by the sign and value of the dot product. Magnitude The length or size of a vector, often found using the square root of the sum of squared components. Angle The measure in degrees or radians between two vectors, used in the alternate dot product formula. Cosine A trigonometric function used in the alternate dot product formula to relate the angle between vectors to their product. Perpendicularity A relationship where two vectors meet at a 90-degree angle, resulting in a dot product of zero. Inverse Cosine A mathematical function used to determine the angle between vectors when the dot product and magnitudes are known. Component Form A way of expressing vectors by listing their values along each axis, such as (x, y) or using i and j notation. Positive Result A dot product outcome indicating vectors are pointing in similar directions, showing strong alignment. Negative Result A dot product outcome indicating vectors are pointing in opposite directions, showing negative alignment. Zero Result A dot product outcome indicating vectors are perpendicular, with no alignment or opposition. Degree Mode A calculator setting required when inputting angles in degrees for trigonometric calculations in the dot product formula.
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