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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 ...
Because the angle of the equilibrant force is opposite of the resultant force, if 180 degrees are added or subtracted to the resultant force's angle, the equilibrant force's angle will be known. Multiplying the resultant force vector by a -1 will give the correct equilibrant force vector: <-10, -8>N x (-1) = <10, 8>N = C.
Graphical placing of the resultant force. In physics and engineering, a resultant force is the single force and associated torque obtained by combining a system of forces and torques acting on a rigid body via vector addition. The defining feature of a resultant force, or resultant force-torque, is that it has the same effect on the rigid body ...
In mathematics, physics, and engineering, a Euclidean vector or simply a vector (sometimes called a geometric vector[1] or spatial vector[2]) is a geometric object that has magnitude (or length) and direction. Euclidean vectors can be added and scaled to form a vector space. A vector quantity is a vector-valued physical quantity, including ...
Stress resultants are defined as integrals of stress over the thickness of a structural element. The integrals are weighted by integer powers the thickness coordinate z (or x3). Stress resultants are so defined to represent the effect of stress as a membrane force N (zero power in z), bending moment M (power 1) on a beam or shell (structure).
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 ...
Dot product. In mathematics, the dot product or scalar product[note 1] is an algebraic operation that takes two equal-length sequences of numbers (usually coordinate vectors), and returns a single number. In Euclidean geometry, the dot product of the Cartesian coordinates of two vectors is widely used. It is often called the inner product (or ...
Euler's first law states that the rate of change of linear momentum p of a rigid body is equal to the resultant of all the external forces Fext acting on the body: [2] Internal forces between the particles that make up a body do not contribute to changing the momentum of the body as there is an equal and opposite force resulting in no net ...