The vector work is one of key concepts of the vector analysis. Various sizes are in physics by the vector work of two other sizes. It is necessary to carry out vector works and transformations on its basis very accurately, following the basic rules.
It is required to you
- directions and lengths of two vectors
Instruction
1. The vector work of a vector of an in three-dimensional space registers in b vector in the form of c = [ab]. At the same time the vector with has to meet to a number of requirements.
2. Vector length with is equal to the work of lengths of vectors of an and b on a sine of the angle between them: |with| = |a| |b| *sin(a^b). A vector with ortogonalen to a vector of an and ortogonalen to b vector. The three of vectors of ABC is right.
3. From these rules it is visible that if vectors of an and b are parallel or lie on one straight line, then their vector work to equally zero vector as the sine of the angle between them is equal to zero. In case of perpendicularity of vectors of an and b the vectors of a, b and c will be perpendicular each other and they can be presented lying on axes of a rectangular Cartesian system of coordinates.
4. That the three of vectors of ABC is right the direction of a vector with can be found by the rule of the right hand. Squeeze a hand in a fist, and then direct a forefinger in the direction of a vector of a forward. Direct a middle finger in the direction of a vector of b. Then the thumb directed up perpendicular to an index and middle finger will specify the direction of a vector of page.