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  2. Parallelogram of force - Wikipedia

    en.wikipedia.org/wiki/Parallelogram_of_force

    When more than two forces are involved, the geometry is no longer a parallelogram, but the same principles apply to a polygon of forces. The resultant force due to the application of a number of forces can be found geometrically by drawing arrows for each force. The parallelogram of forces is a graphical manifestation of the addition of vectors.

  3. Direction cosine - Wikipedia

    en.wikipedia.org/wiki/Direction_cosine

    If vectors u and v have direction cosines (α u, β u, γ u) and (α v, β v, γ v) respectively, with an angle θ between them, their units vectors are ^ = + + (+ +) = + + ^ = + + (+ +) = + +. Taking the dot product of these two unit vectors yield, ^ ^ = + + = ⁡, where θ is the angle between the two unit vectors, and is also the angle between u and v.

  4. Euclidean vector - Wikipedia

    en.wikipedia.org/wiki/Euclidean_vector

    Euclidean vector. 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 ...

  5. Vector algebra relations - Wikipedia

    en.wikipedia.org/wiki/Vector_algebra_relations

    Vector algebra relations. Formulas about vectors in three-dimensional Euclidean space. The following are important identities in vector algebra. Identities that only involve the magnitude of a vector and the dot product (scalar product) of two vectors A · B, apply to vectors in any dimension, while identities that use the cross product (vector ...

  6. Resultant force - Wikipedia

    en.wikipedia.org/wiki/Resultant_force

    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 ...

  7. Lambert's problem - Wikipedia

    en.wikipedia.org/wiki/Lambert's_problem

    Lambert's problem. In celestial mechanics, Lambert's problem is concerned with the determination of an orbit from two position vectors and the time of flight, posed in the 18th century by Johann Heinrich Lambert and formally solved with mathematical proof by Joseph-Louis Lagrange. It has important applications in the areas of rendezvous ...

  8. Dot product - Wikipedia

    en.wikipedia.org/wiki/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 rarely the ...

  9. Vector multiplication - Wikipedia

    en.wikipedia.org/wiki/Vector_multiplication

    Vector multiplication. In mathematics, vector multiplication may refer to one of several operations between two (or more) vectors. It may concern any of the following articles: Dot product – also known as the "scalar product", a binary operation that takes two vectors and returns a scalar quantity. The dot product of two vectors can be ...