01.20.2017. Friday
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 Geometry Two-dimensional geometric shapes⦿ Rhombus⦿ Parallelogram⦿ Trapezoid⦿ Kite⦿ Circle⦿ Circular sector⦿ Circular segment⦿ Area of a Triangle⦿ Squere⦿ Rectangle Three-dimensional geometric shapes⦿ Cube⦿ Sphere⦿ Cylinder⦿ Cone⦿ Prism⦿ Pyramide⦿ Platonic solids Trigonometry⦿ Law of Sines⦿ Law of Cosines⦿ Trygonometry Identities of same angle⦿ Identities for the sum and difference of two angles⦿ Trigonometric identities of double angles⦿ Trigonometric identities of half angles⦿ Sum and difference of trigonometric functions⦿ Trigonometry of right triangles Vectors⦿ Scalar Product of Vectors⦿ Vector Product of Vectors Analytical Geometry 2D⦿ Distance between two points⦿ Circle⦿ Linear equation⦿ Ellipse

Vectors

# Vector Product of Vectors

$\stackrel{\to }{a}={x}_{1}\stackrel{\to }{i}+{y}_{1}\stackrel{\to }{j}+{z}_{1}\stackrel{\to }{k},\phantom{\rule{mediummathspace}{0ex}}\phantom{\rule{mediummathspace}{0ex}}\phantom{\rule{mediummathspace}{0ex}}\phantom{\rule{mediummathspace}{0ex}}\stackrel{\to }{b}={x}_{2}\stackrel{\to }{i}+{y}_{2}\stackrel{\to }{j}+{z}_{2}\stackrel{\to }{k}$
$\stackrel{\to }{c}\perp \stackrel{\to }{a}\wedge \phantom{\rule{thickmathspace}{0ex}}\stackrel{\to }{c}\perp \stackrel{\to }{b}$
$\stackrel{\to }{c}=\stackrel{\to }{a}×\stackrel{\to }{b}=|\begin{array}{}\stackrel{\to }{i}& \stackrel{\to }{j}& \stackrel{\to }{k}\\ {x}_{1}& {y}_{1}& {z}_{1}\\ {x}_{2}& {y}_{2}& {z}_{2}\end{array}|$
$\stackrel{\to }{c}=\left({y}_{1}{z}_{2}-{z}_{1}{y}_{2}\right)\stackrel{\to }{i}+\left({z}_{1}{x}_{2}-{x}_{1}{z}_{2}\right)\stackrel{\to }{j}+\left({x}_{1}{y}_{2}-{y}_{1}{x}_{2}\right)\stackrel{\to }{k}$
$|\stackrel{\to }{c}|=|\stackrel{\to }{a}|·|\stackrel{\to }{b}|·sin\alpha$

The result of vector product, vector c⃗, has a length that is equal with the area of parallelogram between vecrors a⃗ and b⃗ (pink area).