Engineering Calculus Notes 112

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

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: 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 ...
View Full Document

Ask a homework question - tutors are online