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Chapter 15: Vectors in 2D

Chapter 15: Vectors in 2D. Lesson E: Vectors in Coordinate Geometry. Vectors between two points. Consider points A (xA, yA) In going from A to B xB-xA is the x-step yB-yA is the y-step. Y. B. yB. yB-yA. A. yA. xB - xA. X. xA. xB. Vector between two points. Consequently,

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Chapter 15: Vectors in 2D

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  1. Chapter 15: Vectors in 2D Lesson E: Vectors in Coordinate Geometry

  2. Vectors between two points Consider points A (xA, yA) In going from A to B xB-xA is the x-step yB-yA is the y-step Y B yB yB-yA A yA xB - xA X xA xB

  3. Vector between two points • Consequently, • AB = xB – xA yB – yA • if that is AB then BA is?

  4. Vector between two points • Notice • If O is (0,0) and A is (xA, yA) then • OA is xA yA y A(xA, yA) yA O x xA

  5. Distance between two Points • Distance between two points A and B is the length of AB (or BA) and is denoted IABI. • See example #1

  6. Vector Equality • Two vectors are equal if they have the same length and direction • Thus their x-steps are equal i.e., p=r and their y-steps are equal i.e., q=s p r q s = q s p r “If and only if” p=r and q=s

  7. See example

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