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  2. Magnitude (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Magnitude_(mathematics)

    By definition, all Euclidean vectors have a magnitude (see above). However, a vector in an abstract vector space does not possess a magnitude. A vector space endowed with a norm, such as the Euclidean space, is called a normed vector space. [8] The norm of a vector v in a normed vector space can be considered to be the magnitude of v.

  3. Vector notation - Wikipedia

    en.wikipedia.org/wiki/Vector_notation

    A spherical vector is specified by a magnitude, an azimuth angle, and a zenith angle. The magnitude is usually represented as ρ. The azimuth angle, usually represented as θ, is the (counter­clockwise) offset from the positive x-axis. The zenith angle, usually represented as φ, is the offset from the positive z-axis. Both angles are ...

  4. Phasor - Wikipedia

    en.wikipedia.org/wiki/Phasor

    Phasor notation (also known as angle notation) is a mathematical notation used in electronics engineering and electrical engineering.A vector whose polar coordinates are magnitude and angle is written . [13] can represent either the vector (⁡, ⁡) or the complex number ⁡ + ⁡ =, according to Euler's formula with =, both of which have magnitudes of 1.

  5. Angle - Wikipedia

    en.wikipedia.org/wiki/Angle

    [56] [57] Procedurally, the magnitude of the reference angle for a given angle may determined by taking the angle's magnitude modulo ⁠ 1 / 2 ⁠ turn, 180°, or π radians, then stopping if the angle is acute, otherwise taking the supplementary angle, 180° minus the reduced magnitude. For example, an angle of 30 degrees is already a ...

  6. Axis–angle representation - Wikipedia

    en.wikipedia.org/wiki/Axis–angle_representation

    The angle θ and axis unit vector e define a rotation, concisely represented by the rotation vector θe.. In mathematics, the axis–angle representation parameterizes a rotation in a three-dimensional Euclidean space by two quantities: a unit vector e indicating the direction of an axis of rotation, and an angle of rotation θ describing the magnitude and sense (e.g., clockwise) of the ...

  7. Vector projection - Wikipedia

    en.wikipedia.org/wiki/Vector_projection

    The scalar projection is defined as [2] = ‖ ‖ ⁡ = ^ where the operator ⋅ denotes a dot product, ‖a‖ is the length of a, and θ is the angle between a and b. The scalar projection is equal in absolute value to the length of the vector projection, with a minus sign if the direction of the projection is opposite to the direction of b ...

  8. Euclidean vector - Wikipedia

    en.wikipedia.org/wiki/Euclidean_vector

    An example is velocity, the magnitude of which is speed. For instance, the velocity 5 meters per second upward could be represented by the vector (0, 5) (in 2 dimensions with the positive y-axis as 'up'). Another quantity represented by a vector is force, since it has a magnitude and direction and follows the rules of vector addition. [7]

  9. Euler angles - Wikipedia

    en.wikipedia.org/wiki/Euler_angles

    The axes of the original frame are denoted as x, y, z and the axes of the rotated frame as X, Y, Z.The geometrical definition (sometimes referred to as static) begins by defining the line of nodes (N) as the intersection of the planes xy and XY (it can also be defined as the common perpendicular to the axes z and Z and then written as the vector product N = z × Z).