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Geometric Representation of Vectors

Geometric Representation of Vectors. 12.1. Vectors. Vectors are quantities that are described by a direction and a magnitude (size or distance denoted with absolute value).

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Geometric Representation of Vectors

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  1. Geometric Representation of Vectors 12.1

  2. Vectors • Vectors are quantities that are described by a direction and a magnitude (size or distance denoted with absolute value). • Vectors are primarly used in physics. For example, vectors are used for velocity of a plane, a person swimming across a river or a person walking on a moving train.

  3. A 15 B 10 C Addition of Vectors • Given represents the motion of a object 15 units south from A to B, and represents the movement of the object 10 units southeast, we say that is the vector sum of and .

  4. Visually • **NOTE: order is irrelevant when adding vectors A 15 B 10 C

  5. Subtraction of Vectors -v v A negative vector is the same length, but in the opposite direction.

  6. Vectors can be added as well as subtracted. v v w v - w -w Find v – w given: [this also means v + (-w) ]

  7. D C 4 A B Ex. 1: ABCD is a square. Complete each statement.

  8. Multiplication of Vectors v + v = 2v

  9. Ex. 2: • Make a diagram that illustrates a force of 8 N north and a force of 6 N west acting on a body. Illustrate the resultant sum of these 2 forces. Find its strength and determine the direction (W of N) of the force.

  10. Ex. 3: • An airplane has a velocity of 400 mi/h southwest. A 50 mi/h wind is blowing from the west. Find the resultant speed and direction of the plane.

  11. -t r -t r r r r t t t Ex. 4: • Vectors t and r are given. Sketch a) 3r + 2t and b) r – 2t r - 2t 3r + 2t

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