Engineering Calculus Notes 112

# Engineering Calculus Notes 112 - 100 CHAPTER 1 COORDINATES...

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Unformatted text preview: 100 CHAPTER 1. COORDINATES AND VECTORS Thus, a normal vector is →→ − =− ×− n v s →t v →→ −− ı = → − k −2 1 3 1 −2 −1 → − −2 1 +k 1 −2 1 3 → −2 3 −− −2 −1 1 −1 → − →→ = 5− + − + 3 k ı → =− ı and an equation for P ′ is 5(x − 3) + 1(y + 1) + 3(z − 0) = 0 or 5x + y + 3z = 14. Intersection of Planes The line of intersection of two planes can be speciﬁed as the set of simultaneous solutions of two linear equations, one for each plane. How do we ﬁnd a parametrization for this line? Note that a linear equation for a plane Ax + By + Cz = D immediately gives us a normal vector → → − = A− + B − + C − . → → n ı k If we are given two such equations → − → → A1 − + B1 − + C1 k = D1 ı → − → → A − +B − +C k =D ı 2 2 2 2 then the line of intersection ℓ (the locus of this pair of equations) is perpendicular to both normal vectors → → − =A − +B − +C − → → ni iı i ik i = 1, 2, 3 ...
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## 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.

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