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- https://math.libretexts.org/Bookshelves/Linear_Algebra/Linear_Algebra_with_Applications_(Nicholson)/06%3A_Vector_Spaces/6.01%3A_Examples_and_Basic_PropertiesA vector space consists of a nonempty set V of objects (called vectors) that can be added, that can be multiplied by a real number (called a scalar in this context), and for which certain axioms ho...A vector space consists of a nonempty set V of objects (called vectors) that can be added, that can be multiplied by a real number (called a scalar in this context), and for which certain axioms hold.
- https://math.libretexts.org/Courses/De_Anza_College/Calculus_III%3A_Series_and_Vector_Calculus/04%3A_Vectors_in_Space/4.01%3A_Vectors_in_the_PlaneWhen measuring a force, such as the thrust of the plane’s engines, it is important to describe not only the strength of that force, but also the direction in which it is applied. Some quantities, such...When measuring a force, such as the thrust of the plane’s engines, it is important to describe not only the strength of that force, but also the direction in which it is applied. Some quantities, such as or force, are defined in terms of both size (also called magnitude) and direction. A quantity that has magnitude and direction is called a vector.
- https://math.libretexts.org/Courses/SUNY_Schenectady_County_Community_College/A_First_Journey_Through_Linear_Algebra/05%3A_Vector_Spaces/5.11%3A_Supplementary_Notes_-_A_More_In-Depth_Look_at_Vector_Spaces/5.11.01%3A_Vector_Spaces/5.11.1.01%3A_Examples_and_Basic_PropertiesA vector space consists of a nonempty set V of objects (called vectors) that can be added, that can be multiplied by a real number (called a scalar in this context), and for which certain axioms ho...A vector space consists of a nonempty set V of objects (called vectors) that can be added, that can be multiplied by a real number (called a scalar in this context), and for which certain axioms hold.
- https://math.libretexts.org/Bookshelves/Geometry/Geometry_with_an_Introduction_to_Cosmic_Topology_(Hitchman)/02%3A_The_Complex_Plane/2.01%3A_Basic_NotionsThe set of complex numbers is obtained algebraically by adjoining the number i to the set R of real numbers, where i is defined by the property that i^2=−1. We will take a geometric approach and defin...The set of complex numbers is obtained algebraically by adjoining the number i to the set R of real numbers, where i is defined by the property that i^2=−1. We will take a geometric approach and define a complex number to be an ordered pair (x,y) of real numbers.
- https://math.libretexts.org/Bookshelves/Calculus/Calculus_(OpenStax)/12%3A_Vectors_in_Space/12.01%3A_Vectors_in_the_PlaneWhen measuring a force, such as the thrust of the plane’s engines, it is important to describe not only the strength of that force, but also the direction in which it is applied. Some quantities, such...When measuring a force, such as the thrust of the plane’s engines, it is important to describe not only the strength of that force, but also the direction in which it is applied. Some quantities, such as or force, are defined in terms of both size (also called magnitude) and direction. A quantity that has magnitude and direction is called a vector.
- https://math.libretexts.org/Courses/Cosumnes_River_College/Math_375%3A_Pre-Calculus/08%3A_Non-Right_Triangle_Trigonometry/8.04%3A_Vectors_-_A_Geometric_ApproachThis section introduces vectors from a geometric perspective, covering definitions, notation, and operations. It explains position vectors, scalar multiplication, vector addition, and the concepts of ...This section introduces vectors from a geometric perspective, covering definitions, notation, and operations. It explains position vectors, scalar multiplication, vector addition, and the concepts of displacement and resultant vectors. The section also addresses vector components, their magnitudes, and applications in velocity and other contexts. Detailed examples and exercises help illustrate these concepts, providing a comprehensive understanding of vectors in geometric terms.
- https://math.libretexts.org/Courses/University_of_Maryland/MATH_241/01%3A_Vectors_in_Space/1.02%3A_Vectors_in_the_PlaneWhen measuring a force, such as the thrust of the plane’s engines, it is important to describe not only the strength of that force, but also the direction in which it is applied. Some quantities, such...When measuring a force, such as the thrust of the plane’s engines, it is important to describe not only the strength of that force, but also the direction in which it is applied. Some quantities, such as or force, are defined in terms of both size (also called magnitude) and direction. A quantity that has magnitude and direction is called a vector.
- https://math.libretexts.org/Courses/De_Anza_College/Linear_Algebra%3A_A_First_Course/02%3A_Matrices/2.01%3A_Matrix_OperationsYou have now solved systems of equations by writing them in terms of an augmented matrix and then doing row operations on this augmented matrix. It turns out that matrices are important not only for s...You have now solved systems of equations by writing them in terms of an augmented matrix and then doing row operations on this augmented matrix. It turns out that matrices are important not only for systems of equations but also in many applications. In this section, we explore some matrix operations.
- https://math.libretexts.org/Courses/Lake_Tahoe_Community_College/Interactive_Calculus_Q3/04%3A_Vectors_in_Space/4.02%3A_Vectors_in_the_PlaneWhen measuring a force, such as the thrust of the plane’s engines, it is important to describe not only the strength of that force, but also the direction in which it is applied. Some quantities, such...When measuring a force, such as the thrust of the plane’s engines, it is important to describe not only the strength of that force, but also the direction in which it is applied. Some quantities, such as or force, are defined in terms of both size (also called magnitude) and direction. A quantity that has magnitude and direction is called a vector.
- https://math.libretexts.org/Courses/Reedley_College/Trigonometry/04%3A_Further_Applications_of_Trigonometry/4.06%3A_VectorsGround speed refers to the speed of a plane relative to the ground. Airspeed refers to the speed a plane can travel relative to its surrounding air mass. These two quantities are not the same because ...Ground speed refers to the speed of a plane relative to the ground. Airspeed refers to the speed a plane can travel relative to its surrounding air mass. These two quantities are not the same because of the effect of wind. In an earlier section, we used triangles to solve a similar problem involving the movement of boats. Later in this section, we will find the airplane’s ground speed and bearing, while investigating another approach to problems of this type.
- https://math.libretexts.org/Workbench/Algebra_and_Trigonometry_2e_(OpenStax)/10%3A_Further_Applications_of_Trigonometry/10.09%3A_VectorsGround speed refers to the speed of a plane relative to the ground. Airspeed refers to the speed a plane can travel relative to its surrounding air mass. These two quantities are not the same because ...Ground speed refers to the speed of a plane relative to the ground. Airspeed refers to the speed a plane can travel relative to its surrounding air mass. These two quantities are not the same because of the effect of wind. In an earlier section, we used triangles to solve a similar problem involving the movement of boats. Later in this section, we will find the airplane’s ground speed and bearing, while investigating another approach to problems of this type.
