2.10. Mixed product of vectors and its properties

Lecture



The number ( a × b, c ) is called the mixed product of the vectors a, b, c and is denoted by ( a, b, c ) .

If a, b, c are coplanar vectors, then ( a, b, c ) = 0. The modulus of the mixed product of non-coplanar vectors is equal to the volume of the parallelepiped constructed on these vectors.

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Lectures and tutorial on "Linear Algebra and Analytical Geometry"

Terms: Linear Algebra and Analytical Geometry

Quaternion History
1. Elements of linear algebra 1. The determinants of the second and third orders
1. Elements of linear algebra 2. Kramer’s method for solving systems of algebraic equations
2.1. Concept of geometric vector
2.2. Vector module
2.3. Basis of vector and coplanar vectors
2.4. The decomposition of the vector basis
2.5. Right three vectors
2.6. Projection of vector onto vector
2.7. Orthonormal basis
2.8. Scalar product of vectors and its properties
2.9. Vector product of vectors and its properties
2.10. Mixed product of vectors and its properties
3.1. Definition of a rectangular Cartesian coordinate system
3.2. Finding the coordinates of a vector given by two points
3.3. Linear vector operations
3.4. The products of vectors in PDK
3.5. The condition for determining the basis
3.6. Polar coordinates
Elements of analytical geometry 1.4.1. Direct in space
4.2. Plane in space
4.3. Straight line on a plane
4.4. Second order curves
4.5. Ellipse
4.6. Hyperbola
4.7. Parabola
Examples of solving problems to the section Linear algebra and analytic geometry
Matrix and Gram determinant
LINEAR FORM