by andy shen vectors in the plane. two-dimensional vectors
TRANSCRIPT
By Andy Shen
VECTORS IN THE PLANE
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
• 7.a(bu)=(ab)u
• 8.a(u+v)=au+av
• 9.(a+b)u=au+bu
THREE-DIMENSIONAL VECTORS
MAGNITUDE OF A 3D VECTOR
EXAMPLE OF VECTORS IN DIFFERENT PLANES
EXAMPLE 2
GRAPH OF X^2+Y^2=4 IN R^2 AND R^3
THE REALLY COOL PART OF VECTOR IN 3D
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