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The Rectangular Coordinate System
The Geometry of Vectors
Equations of Lines in Space
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A X B angle boundary bounded called Chapter column vectors components compute Consequently constant continuous coordinate system cross product deﬁned deﬁnition denote determinant differential equation diﬂerentiable dot product double integral elements Example Exercise ﬁeld FIGURE ﬁnd ﬁnding ﬁnite number ﬁrst ﬁrst octant formula function deﬁned function F given gives Hence homogeneous inequalities inﬁnite intersection inverse iterated integral left side Let 9 Let F line integral line segment linear equations linear transformation linearly independent linearly independent set matrix multiplication notation obtain orthogonal pair parallel partial derivatives perpendicular polynomial Prove Theorem reader real numbers rectangle region 9 replaced right side row vectors saddle surface satisﬁed scalar Section shown in Fig solution solve sphere suitable Suppose tangent plane Theorem 15 unit vector variables vector function vector space x-axis xy-plane y-axis yz-plane z-axis zero vector