Engineering Calculus Notes 105

Engineering Calculus Notes 105 - 93 1.6 CROSS PRODUCTS C C...

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1.6. CROSS PRODUCTS 93 A B C D A B C D A B C D Figure 1.47: Area Swept Out by DP as P Traverses a Triangle (c) Show that if −→ v i = ( x i ,y i ), i = 0 ,..., 3 with −→ v 0 = −→ v 3 then the signed area of [ −→ v 1 , −→ v 2 , −→ v 3 ] can be calculated as σ ( −→ v 1 −→ v 2 −→ v 3 ) A ( −→ v 1 −→ v 2 −→ v 3 ) = 1 2 3 summationdisplay i =1 vextendsingle vextendsingle vextendsingle vextendsingle x i 1 y i 1 x i y i vextendsingle vextendsingle vextendsingle vextendsingle . 12. (a) Consider the three quadrilaterals in Figure 1.48
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