Engineering Calculus Notes 106

Engineering Calculus Notes 106 - 94 CHAPTER 1 COORDINATES...

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94 CHAPTER 1. COORDINATES AND VECTORS square [ ABCD ] is given by σ ( ABCD ) A ( square [ ABCD ]) = 1 2 braceleftbig ( x 2 x 0 )( y 3 y 1 )+( x 1 x 3 )( y 2 y 0 ) bracerightbig where the coordinates of the vertices are A ( x 0 ,y 0 ) B ( x 1 ,y 1 ) C ( x 2 ,y 2 ) D ( x 3 ,y 3 ) . Note that this is the same as 1 2 Δ ( −→ v, −→ w ) where −→ v = −→ AC and −→ w = −−→ DA are the diagonal vectors of the quadrilateral. (c) What should be the (signed) area of the oriented quadrilateral square [ ABCD ] in Figure 1.49 ? A B C D Figure 1.49: Signed Area of Quadrangles (2)
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