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Vector projection. The vector projection (also known as the vector component or vector resolution) of a vector a on (or onto) a nonzero vector b is the orthogonal projection of a onto a straight line parallel to b. The projection of a onto b is often written as or a∥b. The vector component or vector resolute of a perpendicular to b, sometimes ...
In mathematics, the cross product or vector product (occasionally directed area product, to emphasize its geometric significance) is a binary operation on two vectors in a three-dimensional oriented Euclidean vector space (named here ), and is denoted by the symbol . Given two linearly independent vectors a and b, the cross product, a × b ...
Rotation matrix. In linear algebra, a rotation matrix is a transformation matrix that is used to perform a rotation in Euclidean space. For example, using the convention below, the matrix. rotates points in the xy plane counterclockwise through an angle θ about the origin of a two-dimensional Cartesian coordinate system.
In mathematics, a rotation of axes in two dimensions is a mapping from an xy - Cartesian coordinate system to an x′y′ -Cartesian coordinate system in which the origin is kept fixed and the x′ and y′ axes are obtained by rotating the x and y axes counterclockwise through an angle . A point P has coordinates (x, y) with respect to the ...
The aerodynamic force is the resultant vector from adding the lift vector, perpendicular to the flow direction, and the drag vector, parallel to the flow direction. Forces on an aerofoil. In fluid mechanics, an aerodynamic force is a force exerted on a body by the air (or other gas) in which the body is immersed, and is due to the relative ...
One may wish to express rotation as a rotation vector, or Euler vector, an un-normalized three-dimensional vector the direction of which specifies the axis, and the length of which is θ, = ^. The rotation vector is useful in some contexts, as it represents a three-dimensional rotation with only three scalar values (its components ...
Transformation matrix. In linear algebra, linear transformations can be represented by matrices. If is a linear transformation mapping to and is a column vector with entries, then for some matrix , called the transformation matrix of . [citation needed] Note that has rows and columns, whereas the transformation is from to .
Direction cosine. In analytic geometry, the direction cosines (or directional cosines) of a vector are the cosines of the angles between the vector and the three positive coordinate axes. Equivalently, they are the contributions of each component of the basis to a unit vector in that direction.