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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/Bookshelves/Linear_Algebra/Map%3A_Linear_Algebra_(Waldron_Cherney_and_Denton)/01%3A_What_is_Linear_Algebra/1.01%3A_What_Are_VectorsVectors are things you can add and scalar multiply.
- 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/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/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/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/Differential_Equations_and_Linear_Algebra_(Zook)/04%3A_R/4.03%3A_Geometric_Meaning_of_Vector_AdditionThen \(\vec{u}+\vec{v}\) is the vector which results from drawing a vector from the tail of \(\vec{u}\) to the tip of \(\vec{v}\). Next consider \(\vec{u}-\vec{v}.\) This means \(\vec{u}+\left( -\vec{...Then \(\vec{u}+\vec{v}\) is the vector which results from drawing a vector from the tail of \(\vec{u}\) to the tip of \(\vec{v}\). Next consider \(\vec{u}-\vec{v}.\) This means \(\vec{u}+\left( -\vec{v} \right) .\) From the above geometric description of vector addition, \(-\vec{v}\) is the vector which has the same length but which points in the opposite direction to \(\vec{v}\).
- https://math.libretexts.org/Under_Construction/Purgatory/Differential_Equations_and_Linear_Algebra_(Zook)/08%3A_What_is_Linear_Algebra/8.01%3A_What_Are_VectorsVectors are things you can add and scalar multiply.
- 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.
- https://math.libretexts.org/Bookshelves/Algebra/Algebra_and_Trigonometry_1e_(OpenStax)/10%3A_Further_Applications_of_Trigonometry/10.08%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.
