Engineering Calculus Notes 105

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

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 93 1.6. CROSS PRODUCTS C C B A C • D B D• B A A •D Figure 1.47: Area Swept Out by DP as P Traverses a Triangle → → → (c) Show that if − i = (xi , yi ), i = 0, . . . , 3 with − 0 = − 3 then the v v v →→→ − , − , − ] can be calculated as signed area of [ v 1 v 2 v 3 1 →→→ →→→ σ ( − 1 − 2 − 3 ) A ( △− 1 − 2 − 3 ) = vvv vvv 2 3 i=1 x i− 1 y i− 1 . xi yi 12. (a) Consider the three quadrilaterals in Figure 1.48. In all three D D C C C A D B B A B A Figure 1.48: Signed Area of Quadrangles cases, the orientation of [ABCD ] and of △ABC is positive, but the orientation of △ACD is not necessarily positive. Show that in all three cases, A ( ABCD ) = σ (ABC ) A (△ABC ) + σ (ACD ) A (△ACD ) . (b) Use this to show that the signed area of a quadrilateral ...
View Full Document

This note was uploaded on 10/20/2011 for the course MAC 2311 taught by Professor All during the Fall '08 term at University of Florida.

Ask a homework question - tutors are online