Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Line (geometry) wikipedia , lookup
Mathematics of radio engineering wikipedia , lookup
Minkowski space wikipedia , lookup
Vector space wikipedia , lookup
Classical Hamiltonian quaternions wikipedia , lookup
Bra–ket notation wikipedia , lookup
Euclidean vector wikipedia , lookup
Objective: Find the components of a vector. Number plane, or Cartesian coordinate system – a plane determined by the horizontal line called the xaxis and a vertical line called the y-axis intersecting at right angles. Plane divided in two four quadrants: I, II, III, and IV. Vector drawings A directed line segment; arrowhead indicates direction Length indicates magnitude Starts with initial point Ends with terminal point, or end point R The sum of two or more vectors is called the resultant vector. When two or more vectors are added are added, each vector is called a component vector. Useful component vectors are the components that are both perpendicular and that are parallel to the x- and y-axes. The horizontal component is called the x-component. The vertical component is called the y-component. R Ry Rx The x- and y-components can be expressed as signed numbers. Absolute value indicates magnitude of vector. The sign indicates the direction. x-component y-component +, if right +, if up -, if left -, if down Find the x- and y-components of vector R. R Find the x- and y-components of vector v. v Find the x- and y-components of vector u. u We can find the resultant of several vectors using arithmetic graphing. The sum of all x-components for each vector gives the x- component for the resultant vector, Rx. The sum of all y-components for each vector gives the ycomponent for the resultant vector, Ry. R A Ax = +3 B By = +4 By = +2 Ay = +2 Vector x-comp y-comp A +3 +2 B +2 +4 R +5 +6 Given vectors A, B, and C, graph and find the x- and ycomponents of the resultant vector R. Vector A C B B C R A x-comp y-comp Two vectors are equal when they have the same magnitude and the same direction. They are opposites or negatives of each other when they have the same magnitude but opposite direction A vector may be placed in any position in the number plane as long as its magnitude and direction are not changed. To add two or more vector graphically: 1. Draw first vector with initial point at origin 2. The second vector should be drawn with its initial point on the on the end point of first vector 3. If there are more vectors repeat until the last one drawn. 4. The sum, or the resultant vector, is drawn by joining the initial point of the first vector to the end point of the last vector. Note: the order in which the vector are added does not matter. Given vectors A, B, and C, graph and find the x- and ycomponents of the resultant vector R. B A B A R C C Rx = +1 Ry = -5