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2.2 Components of a Vector

2.2 Components of a Vector. Objective: Find the components of a vector. Number plane, or Cartesian coordinate system – a plane determined by the horizontal line called the x-axis and a vertical line called the y-axis intersecting at right angles.

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2.2 Components of a Vector

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  1. 2.2Components of a Vector Objective: Find the components of a vector.

  2. Number plane, or Cartesian coordinate system – a plane determined by the horizontal line called the x-axis and a vertical line called the y-axis intersecting at right angles. • Plane divided in two four quadrants: I, II, III, and IV.

  3. Vector drawings • A directed line segment; arrowhead indicates direction • Length indicates magnitude • Starts with initial point • Ends with terminal point, or end point R

  4. 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.

  5. 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

  6. The x- and y-components can be expressed as signed numbers. • Absolute value indicates magnitude of vector. • The sign indicates the direction.

  7. Find the x- and y-components of vector R. R

  8. Find the x- and y-components of vector v. v

  9. Find the x- and y-components of vector u. u

  10. 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 y-component for the resultant vector, Ry. By = +4 R B By = +2 A Ay = +2 Ax = +3

  11. Given vectors A, B, and C, graph and find the x- and y-components of the resultant vector R. C B A

  12. 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.

  13. To add two or more vector graphically: • Draw first vector with initial point at origin • The second vector should be drawn with its initial point on the on the end point of first vector • If there are more vectors repeat until the last one drawn. • 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.

  14. Given vectors A, B, and C, graph and find the x- and y- components of the resultant vector R. B B A A R C C Rx = +1 Ry = -5

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