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Lines and planes
The cross product
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3-dimensional 3-space A X B assume boundary centered chain rule change of variables Chapter circle of radius column vector component Compute constant continuous function cos2 definition denote differentiable curve differentiable function differential operator direction dot product dx dy dy dx Example Exercises exists expression Figure Find the integral Find the volume finite number Fourier Fourier series function defined grad grad/(P Green's theorem Hence implicit function inequalities integral of F interval inverse mapping Jacobian matrix length Let F Let F(x Let G Let X(t line segment linear map located vector map G multiple n-tuples notation number of smooth obtain open set parallelogram spanned parametric equation partial derivatives perpendicular polar coordinates potential function Proof prove rectangle region bounded satisfies scalar product set of points Show Similarly sphere of radius square surface unit vector variables formula vector field write