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Vectors in the planE

Vectors in the planE. By Andy Shen. Two-dimensional vectors. Vector properties. Magnitude of a 2d vector. Direction of a 2d vector. Properties of vector operations. Let u,v,w be vectors and a,b be scalars 1. u+v = v+u 2.( u+v )+w=u+( v+w ) 3.u+0=u 4.u+(-u)=0 5.0u=0 6.1u=u

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Vectors in the planE

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  1. Vectors in the planE By Andy Shen

  2. Two-dimensional vectors

  3. Vector properties

  4. Magnitude of a 2d vector

  5. Direction of a 2d vector

  6. Properties of vector operations • Let u,v,w be vectors and a,b be scalars • 1. u+v=v+u • 2.(u+v)+w=u+(v+w) • 3.u+0=u • 4.u+(-u)=0 • 5.0u=0 • 6.1u=u • 7.a(bu)=(ab)u • 8.a(u+v)=au+av • 9.(a+b)u=au+bu

  7. Three-dimensional vectors

  8. Magnitude of a 3d vector

  9. Example of vectors in different planes

  10. Example 2

  11. Graph of x^2+y^2=4 in r^2 and r^3

  12. The really cool part of vector in 3d

  13. End Thank you Links:http://www.intmath.com/vectors/7-vectors-in-3d-space.php, http://tutorial.math.lamar.edu/Classes/CalcII/3DSpace.aspx, http://tutorial.math.lamar.edu/Classes/CalcII/VectorsIntro.aspx, https://www.khanacademy.org/math/calculus/multivariable-calculus/3d_flux/v/conceputal-understanding-of-flux-in-three-dimensions

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