By Andy Shen VECTORS IN THE PLANE. TWO-DIMENSIONAL VECTORS.
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Transcript of By Andy Shen VECTORS IN THE PLANE. TWO-DIMENSIONAL VECTORS.
![Page 1: By Andy Shen VECTORS IN THE PLANE. TWO-DIMENSIONAL VECTORS.](https://reader036.fdocuments.net/reader036/viewer/2022062314/56649f155503460f94c2ad2b/html5/thumbnails/1.jpg)
By Andy Shen
VECTORS IN THE PLANE
![Page 2: By Andy Shen VECTORS IN THE PLANE. TWO-DIMENSIONAL VECTORS.](https://reader036.fdocuments.net/reader036/viewer/2022062314/56649f155503460f94c2ad2b/html5/thumbnails/2.jpg)
TWO-DIMENSIONAL VECTORS
![Page 3: By Andy Shen VECTORS IN THE PLANE. TWO-DIMENSIONAL VECTORS.](https://reader036.fdocuments.net/reader036/viewer/2022062314/56649f155503460f94c2ad2b/html5/thumbnails/3.jpg)
VECTOR PROPERTIES
![Page 4: By Andy Shen VECTORS IN THE PLANE. TWO-DIMENSIONAL VECTORS.](https://reader036.fdocuments.net/reader036/viewer/2022062314/56649f155503460f94c2ad2b/html5/thumbnails/4.jpg)
MAGNITUDE OF A 2D VECTOR
![Page 5: By Andy Shen VECTORS IN THE PLANE. TWO-DIMENSIONAL VECTORS.](https://reader036.fdocuments.net/reader036/viewer/2022062314/56649f155503460f94c2ad2b/html5/thumbnails/5.jpg)
DIRECTION OF A 2D VECTOR
![Page 6: By Andy Shen VECTORS IN THE PLANE. TWO-DIMENSIONAL VECTORS.](https://reader036.fdocuments.net/reader036/viewer/2022062314/56649f155503460f94c2ad2b/html5/thumbnails/6.jpg)
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
![Page 7: By Andy Shen VECTORS IN THE PLANE. TWO-DIMENSIONAL VECTORS.](https://reader036.fdocuments.net/reader036/viewer/2022062314/56649f155503460f94c2ad2b/html5/thumbnails/7.jpg)
THREE-DIMENSIONAL VECTORS
![Page 8: By Andy Shen VECTORS IN THE PLANE. TWO-DIMENSIONAL VECTORS.](https://reader036.fdocuments.net/reader036/viewer/2022062314/56649f155503460f94c2ad2b/html5/thumbnails/8.jpg)
MAGNITUDE OF A 3D VECTOR
![Page 9: By Andy Shen VECTORS IN THE PLANE. TWO-DIMENSIONAL VECTORS.](https://reader036.fdocuments.net/reader036/viewer/2022062314/56649f155503460f94c2ad2b/html5/thumbnails/9.jpg)
EXAMPLE OF VECTORS IN DIFFERENT PLANES
![Page 10: By Andy Shen VECTORS IN THE PLANE. TWO-DIMENSIONAL VECTORS.](https://reader036.fdocuments.net/reader036/viewer/2022062314/56649f155503460f94c2ad2b/html5/thumbnails/10.jpg)
EXAMPLE 2
![Page 11: By Andy Shen VECTORS IN THE PLANE. TWO-DIMENSIONAL VECTORS.](https://reader036.fdocuments.net/reader036/viewer/2022062314/56649f155503460f94c2ad2b/html5/thumbnails/11.jpg)
GRAPH OF X^2+Y^2=4 IN R^2 AND R^3
![Page 12: By Andy Shen VECTORS IN THE PLANE. TWO-DIMENSIONAL VECTORS.](https://reader036.fdocuments.net/reader036/viewer/2022062314/56649f155503460f94c2ad2b/html5/thumbnails/12.jpg)
THE REALLY COOL PART OF VECTOR IN 3D
![Page 13: By Andy Shen VECTORS IN THE PLANE. TWO-DIMENSIONAL VECTORS.](https://reader036.fdocuments.net/reader036/viewer/2022062314/56649f155503460f94c2ad2b/html5/thumbnails/13.jpg)
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