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  2. Vector projection - Wikipedia

    en.wikipedia.org/wiki/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 proj b ⁡ a {\displaystyle \operatorname {proj} _{\mathbf {b} }\mathbf {a} } or a ∥ b .

  3. Vector (mathematics and physics) - Wikipedia

    en.wikipedia.org/wiki/Vector_(mathematics_and...

    These operations and associated laws qualify Euclidean vectors as an example of the more generalized concept of vectors defined simply as elements of a vector space. Vectors play an important role in physics: the velocity and acceleration of a moving object and the forces acting on it can all be described with vectors. [7]

  4. Resolution (algebra) - Wikipedia

    en.wikipedia.org/wiki/Resolution_(algebra)

    In mathematics, and more specifically in homological algebra, a resolution (or left resolution; dually a coresolution or right resolution [1]) is an exact sequence of modules (or, more generally, of objects of an abelian category) that is used to define invariants characterizing the structure of a specific module or object of this category.

  5. Scalar projection - Wikipedia

    en.wikipedia.org/wiki/Scalar_projection

    If 0° ≤ θ ≤ 90°, as in this case, the scalar projection of a on b coincides with the length of the vector projection. Vector projection of a on b (a 1), and vector rejection of a from b (a 2).

  6. Euclidean vector - Wikipedia

    en.wikipedia.org/wiki/Euclidean_vector

    Vectors also describe many other physical quantities, such as linear displacement, displacement, linear acceleration, angular acceleration, linear momentum, and angular momentum. Other physical vectors, such as the electric and magnetic field, are represented as a system of vectors at each point of a physical space; that is, a vector field ...

  7. Gasoline Linked to 150 Million Cases of Mental Health ...

    www.aol.com/lifestyle/gasoline-linked-150...

    A new study says that exhaust from gasoline containing lead may have contributed to ADHD, anxiety, and other mental health disorders in a large segment of the population

  8. FBI, DHS leaders decline to testify publicly about threats ...

    www.aol.com/news/fbi-dhs-leaders-decline-testify...

    WASHINGTON (Reuters) -FBI Director Christopher Wray and Homeland Security Secretary Alejandro Mayorkas declined to appear publicly on Thursday before a U.S. Senate committee to discuss national ...

  9. Resolution of singularities - Wikipedia

    en.wikipedia.org/wiki/Resolution_of_singularities

    In algebraic geometry, the problem of resolution of singularities asks whether every algebraic variety V has a resolution, which is a non-singular variety W with a proper birational map W→V. For varieties over fields of characteristic 0 , this was proved by Heisuke Hironaka in 1964; [ 1 ] while for varieties of dimension at least 4 over ...