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Vectors

Vectors. Vector representation. Vectors quantities have both magnitude and direction and so are represented by arrows . A quantity that does not have a direction is called a scalar quantity. Vectors. Size of arrow – gives magnitude of vector. Angle of arrow – gives direction of vector.

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Vectors

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  1. Vectors

  2. Vector representation Vectors quantities have both magnitude and direction and so are represented by arrows. A quantity that does not have a direction is called a scalar quantity.

  3. Vectors Size of arrow – gives magnitude of vector. Angle of arrow – gives direction of vector. - This is the velocity vector of a cheetah running (10m/s at an angle of 350 North of East) - Vectors can be moved around without changing its magnitude or direction.

  4. Examples Some Vector examples are: Displacement Velocity Acceleration Weight Force Scalar Examples are: Distance, speed, mass, area, volume, density.

  5. Vector addition rule • Vectors can be added. When adding the tail of the second vector must touch the head of the first vector. - Multiple vectors can be added this way. - The resultant vector is the sum of all vectors. It results from connecting the tail of the firstvector with the head of the last vector.

  6. Graphical addition of vectors Example of multiple vector addition: The Blue vector is the resultant vector that represents all vectors added together.

  7. Displacement and velocity Vectors If the green and blue vectors represent displacement vectors, then the pink vector represents the RESULTANT or displacement vector. If the green and blue vectors represent velocity vectors, then the pink vector represents the RESULTANT or velocity vector.

  8. Vector Subtraction - Vectors can be subtracted by adding the first vector to its second negative vector. - Vector (A-B) is actually [A+(-B)] - Vectors can be subtracted both graphically and mathematically. Follow the same rule as addition, except substitute the subtracting vector with its negative vector. - A negative vector has the same magnitude as the positive vector. Only its direction changes.

  9. Mathematical addition of vectors When vectors are at 900 to each other, it is easier to find the resultant vector by using mathematical equations. If two sides are given, then use the Pythagorean theorem to find the third side. C2 = A2 + B2 To find angles use trigonometry. Sinθ=Opp/Hyp ; Cosθ=Adj/Hyp & tanθ=Opp/Adj (SOH CAH TOA)

  10. X and Y Components of vectors A vector can be defined by its X & Y components. Here the actual vector (pink arrow) can also be represented by its x-component (green arrow) & y-component (blue arrow).

  11. X and Y Components of vectors Using the trigonometry, - the x-component by Vx = V(CosØ) - And the y-component by Vy = V(SinØ) and if Vx and Vy are given, then find V, using V2 = Vx2 + Vy2

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