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4.1: Vector Arithmetic
https://phys.libretexts.org/Bookshelves/Electricity_and_Magnetism/Electromagnetics_I_(Ellingson)/04%3A_Vector_Analysis/4.01%3A_Vector_Arithmetic
In mathematical notation, a real-valued vector A is said to have a magnitude A=|A| and direction a^ such that A=Aa^(4.1.1) where a^ is a unit vector (i.e., a real-valued vector having magnitud...In mathematical notation, a real-valued vector A is said to have a magnitude A=|A| and direction a^ such that A=Aa^(4.1.1) where a^ is a unit vector (i.e., a real-valued vector having magnitude equal to one) having the same direction as A . If a vector is complex-valued, then A is similarly complex-valued
19.3: Appendix - Vector algebra
https://phys.libretexts.org/Bookshelves/Classical_Mechanics/Variational_Principles_in_Classical_Mechanics_(Cline)/19%3A_Mathematical_Methods_for_Classical_Mechanics/19.03%3A_Appendix_-_Vector_algebra
Scalar, vector, tensor products of linear operators.
10: The Dot Product
https://phys.libretexts.org/Courses/Prince_Georges_Community_College/General_Physics_I%3A_Classical_Mechanics/10%3A_The_Dot_Product
We begin to look at vector multiplication starting in this chapter with the dot product, sometimes called the scalar product because it multiplied two vectors together to yield a scalar.
3.8: Products of Vectors (Part 1)
https://phys.libretexts.org/Courses/Joliet_Junior_College/Physics_201_-_Fall_2019v2/Book%3A_Custom_Physics_textbook_for_JJC/03%3A_Vectors/3.08%3A_Products_of_Vectors_(Part_1)
One kind of vector multiplication is the scalar product, also known as the dot product, which results in a number (scalar). The scalar product has the distributive property and the commutative propert...One kind of vector multiplication is the scalar product, also known as the dot product, which results in a number (scalar). The scalar product has the distributive property and the commutative property, and is obtained by multiplying the magnitudes of the two vectors with the cosine of the angle between them. This type of vector multiplication is used to find angles between vectors and in the definitions of derived scalar physical quantities such as work or energy.
5.4.2: Work Done by a Constant Force
https://phys.libretexts.org/Courses/Joliet_Junior_College/JJC_-_PHYS_110/05%3A_Book-_Physics_(Boundless)/5.04%3A_Work_and_Energy/5.4.02%3A_Work_Done_by_a_Constant_Force
The work done by a constant force is proportional to the force applied times the displacement of the object.
66.16: Vector Arithmetic
https://phys.libretexts.org/Courses/Prince_Georges_Community_College/General_Physics_I%3A_Classical_Mechanics/66%3A_Appendices/66.16%3A_Vector_Arithmetic
where $\mathbf{i}$ is a unit vector (a vector of magnitude 1) in the $x$ direction, $\mathbf{j}$ is a unit vector in the $y$ direction, and $\mathbf{k}$ is a unit vector in the $z$ directi...where $\mathbf{i}$ is a unit vector (a vector of magnitude 1) in the $x$ direction, $\mathbf{j}$ is a unit vector in the $y$ direction, and $\mathbf{k}$ is a unit vector in the $z$ direction. $A_{x}, A_{y}$ , and $A_{z}$ are called the $x, y$ , and $z$ components (respectively) of vector $\mathbf{A}$ , and are the projections of the vector onto those axes.
10.1: Definition
https://phys.libretexts.org/Courses/Prince_Georges_Community_College/General_Physics_I%3A_Classical_Mechanics/10%3A_The_Dot_Product/10.01%3A_Definition
The dot product of two vectors $\mathbf{A}$ and $\mathbf{B}$ (written $\mathbf{A} \cdot \mathbf{B}$ , and pronounced "A dot $\mathbf{B}$ ") is defined to be the product of their magnitudes, tim...The dot product of two vectors $\mathbf{A}$ and $\mathbf{B}$ (written $\mathbf{A} \cdot \mathbf{B}$ , and pronounced "A dot $\mathbf{B}$ ") is defined to be the product of their magnitudes, times the cosine of the angle between them: It turns out that this combination occurs frequently in physics; the dot product is related to the projection of one vector onto the the other.
7.10: Work Done by a Constant Force
https://phys.libretexts.org/Courses/Joliet_Junior_College/Physics_201_-_Fall_2019/Book%3A_Physics_(Boundless)/07%3A_Work_and_Energy/7.10%3A_Work_Done_by_a_Constant_Force
The work done by a constant force is proportional to the force applied times the displacement of the object.
4.1: Vector Arithmetic
https://phys.libretexts.org/Courses/Berea_College/Electromagnetics_I/04%3A_Vector_Analysis/4.01%3A_Vector_Arithmetic
In mathematical notation, a real-valued vector A is said to have a magnitude A=|A| and direction a^ such that A=Aa^(4.1.1) where a^ is a unit vector (i.e., a real-valued vector having magnitud...In mathematical notation, a real-valued vector A is said to have a magnitude A=|A| and direction a^ such that A=Aa^(4.1.1) where a^ is a unit vector (i.e., a real-valued vector having magnitude equal to one) having the same direction as A . If a vector is complex-valued, then A is similarly complex-valued
10.3: Properties
https://phys.libretexts.org/Courses/Prince_Georges_Community_College/General_Physics_I%3A_Classical_Mechanics/10%3A_The_Dot_Product/10.03%3A_Properties
For example, dotting a vector $\mathbf{A}$ with any of the cartesian unit vectors gives the projection of $\mathbf{A}$ in that direction: In general, the projection of vector $\mathbf{A}$ in the...For example, dotting a vector $\mathbf{A}$ with any of the cartesian unit vectors gives the projection of $\mathbf{A}$ in that direction: In general, the projection of vector $\mathbf{A}$ in the direction of unit vector $\hat{\mathbf{u}}$ is $\mathbf{A} \cdot \hat{\mathbf{u}}$ . From Eq. (7.2.6), it follows that $\mathbf{A} \cdot \mathbf{A}=A_{x}^{2}+A_{y}^{2}+A_{z}^{2}=A^{2}$ ; so the magnitude of a vector $\mathbf{A}$ is given in terms of the dot product by
6.2: Work Done by a Constant Force
https://phys.libretexts.org/Bookshelves/University_Physics/Physics_(Boundless)/6%3A_Work_and_Energy/6.2%3A_Work_Done_by_a_Constant_Force
The work done by a constant force is proportional to the force applied times the displacement of the object.

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