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Math 43 Vectors Resources Resources for Vectors in 2 dimensions and Vectors, Lines, and Planes in 2 and 3 dimensions
We used the "DIAGONAL METHOD" for calculating cross products
Our textbook shows a method of calculating cross products using determinants
The two links immediately below explain both methods, which both give the same result.
Cross Product: Explanations of geometric definition and algebraic definition
Includes both Diagonal Method and Determinant Method
http://www.rose-hulman.edu/media/89572/lccross_productguide.pdf
Cross Product: Algebraic definition calculations only
Includes both Diagonal Method and Determinant Method
http://www.math.mcmaster.ca/~mcleac3/math1ZA3/ExtraNotes/DeterminantSim.pdf
Comparison of dot product and cross product; definitions, properties, and applications
http://nebula.deanza.edu/~bloom/Math43/DotandCrossProductProperties.pdf
Proofs for Dot Product and for Cross Product
of Equivalency of the Algebraic and Geometric definitions
http://nebula.deanza.edu/~bloom/Math43/Dot-Cross-Product-Proofs.pdf
Resources below are short videos on selected topics for vectors, planes and lines in 3 dimensions
Videos from Prof. Larry Green at Lake Tahoe Community College and from Patrickjmt, a professor at at Austin Community College in Texas
Plane Vectors: Chapter 6.3
Finding the Unit Vector in the Direction of Another Vector
http://www.ltcconline.net/greenl/courses/107/videos/vectors/planeVectors/unit/unit.htm
Vector Addition and Scalar Multiplication and the Geometric Interpretation
http://www.ltcconline.net/greenl/courses/107/videos/vectors/planeVectors/addition/addition.htm
Using Vectors to Find the Airspeed of an Airplane
http://www.ltcconline.net/greenl/courses/107/videos/vectors/planeVectors/application/application.htm
3 Dimensional Space: Chapter 11.1
Plotting a Point in the xyz-Space
http://www.ltcconline.net/greenl/courses/107/videos/vectors/3D/plotPoint/plotPoint.htm
Describing a Surface that is the Outside of a Sphere
http://www.ltcconline.net/greenl/courses/107/videos/vectors/3D/sphere/sphere.htm
3 Dimensional Space: Chapter 11.2
Determine if Three Points are Collinear
http://www.ltcconline.net/greenl/courses/107/videos/vectors/3D/collinear/collinear.htm
The Dot Product: Chapter 6.4, 11.2
Finding the Angle Between Two Vectors
http://www.ltcconline.net/greenl/courses/107/videos/vectors/dot/angle/angle.htm
Finding Vectors that are Orthogonal to a Given Vector
http://www.ltcconline.net/greenl/courses/107/videos/vectors/dot/orthogonal/orthogonal.htm
Determining if a Triangle is Acute, Obtuse, or Right
http://www.ltcconline.net/greenl/courses/107/videos/vectors/dot/triangle/triangle.htm
Finding the Projection of u Onto v and the Component of u Orthogonal to v
http://www.ltcconline.net/greenl/courses/107/videos/vectors/dot/proj/proj.htm
Finding the Work Done on and Object
http://www.ltcconline.net/greenl/courses/107/videos/vectors/dot/work/work.htm
The Cross Product: Chapter 11.3
Note that these videos use the determinant method of finding the cross product.
You could also use the diagonal method of finding the cross product.
Finding the Area of a Parallelogram
http://www.ltcconline.net/greenl/courses/107/videos/vectors/cross/area/area.htm
Finding the Volume of a Parallelepiped
http://www.ltcconline.net/greenl/courses/107/videos/vectors/cross/volume/volume.htm
Lines and Planes: Chapter 11.4
Finding the Equation of a Line that is Parallel to a Given Line
http://www.ltcconline.net/greenl/courses/107/videos/vectors/cross/volume/volume.htm
Finding the Equation of a Line
http://www.youtube.com/watch?v=QY15VEK9slo
Finding the Point of Intersection of Two Lines
http://www.ltcconline.net/greenl/courses/107/videos/vectors/linePlane/lineInt/lineInt.htm
Finding the Equation of a Plane that Passes Through Three Given Points
http://www.ltcconline.net/greenl/courses/107/videos/vectors/linePlane/planeEq/planeEq.htm
Sketching a Plane
http://www.ltcconline.net/greenl/courses/107/videos/vectors/linePlane/planeGraph/planeGraph.htm
Finding the Distance Between a Point and a Plane
http://www.ltcconline.net/greenl/courses/107/videos/vectors/linePlane/planePointDist/planePointDist.htm
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