## Vector calculus |

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A X B addition and multiplication algebra angle augmented matrix axis B X C basis vectors called coefﬁcients commutative consider coordinate system corresponding curve deﬁned Deﬁnition determinant diagonal differential directional derivative domain double integral dxdy elements Evaluate Example EXERCISE exists ﬁnd Find the equation ﬁnding ﬁnite function f given Green’s theorem Hence i j k identiﬁed implication independent of path inner product intersection inverse jacobian line integral linear combination linear equations linear transformation linearly dependent obtain one-to-one operations of addition ordered pairs outer product parametric equations partial derivatives perpendicular Proof proposition Prove radius rational number real numbers region respect satisﬁed Show solution solve square matrix subset surface symbolized tangent line three-space triangle triple unit vector upper bound vector function vector parallel write xy plane zero