To find the domain of a vector function, we’ll need to find the domain of the individual components a, b and c. Then the domain of the vector function is the values for which the domains of a, b, and c overlap.
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To find the derivative of a vector function, we just need to find the derivatives of the coefficients when the vector function is in the form r(t)=(r(t)1)i+(r(t)2)j+(r(t)3)k. The derivative function will be in the same form, just with the derivatives of each coefficient replacing the coefficients themselves.
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To find curvature of a vector function, we need the derivative of the vector function, the magnitude of the derivative, the unit tangent vector, its derivative, and the magnitude of its derivative. Once we have all of these values, we can use them to find the curvature.
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When two three-dimensional surfaces intersect each other, the intersection is a curve. We can find the vector equation of that intersection curve using three steps.
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