unit vector

Noun

Meaning

unit vector (plural unit vectors)

(linear algebra, mathematical analysis) A vector with the length of 1, defined as






u
^



=



u


‖

u

‖





{\displaystyle \mathbf {\hat {u}} ={\frac {\mathbf {u} }{\|\mathbf {u} \|}}}

.

Examples

Acceleration vector seeAlso From the heliocentric point of view consider the vector to the planet where is the distance to the planet and is a unit vector pointing towards the planet. Source: Internet

I is defined picking the unit vector that maximizes the flow around the point, because the true flow is maximized across the disk that is perpendicular to it. Source: Internet

Here, the imaginary unit is the (four-dimensional) volume element, and is the unit vector in time direction. Source: Internet

More precisely, when H is differentiable, the dot product of the gradient of H with a given unit vector is equal to the directional derivative of H in the direction of that unit vector. Source: Internet

Also length of a unit vector (of dimension length, not length/force, etc.) has no coordinate-system-invariant significance. Source: Internet

Often this is done to turn the problem into the computation of a directional derivative in the direction of a unit vector. Source: Internet

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