To find the integral of a vector function r(t)=(r(t)1)i+(r(t)2)j+(r(t)3)k, we simply replace each coefficient with its integral. In other words, the integral of the vector function comes in the same form, just with each coefficient replaced by its own integral.
Read MoreTo find the arc length of the vector function, we’ll need to use a specific arc length formula for L that integrates the root of the sum of the squared derivatives. L will be the arc length of the vector function, [a,b] is the interval that defines the arc, and dx/dt, dy/dt, and dz/dt are the derivatives of the parametric equations of x, y, and z respectively.
Read MoreTo find the unit tangent vector for a vector function, we use the formula T(t)=(r'(t))/(||r'(t)||), where r'(t) is the derivative of the vector function and t is given. We’ll start by finding the derivative of the vector function, and then we’ll find the magnitude of the derivative. Those two values will give us everything we need in order to build the expression for the unit tangent vector.
Read MoreTo find curvature at a particular point, we’ll 1) Find r'(t) and use it to 2) Find |r'(t)| and then use r'(t) and |r'(t)| to 3) Find T(t), and then use it to 4) Find T'(t), and then use it to 5) Find |T'(t)|, and then use |r'(t)| and |T'(t)| to 6) Find curvature at the point t that we’re interested in.
Read MoreTo find the scalar equation of a line, we’ll use the formulas x=x_0+at, y=y_0+bt, and z=z_0+ct, where P_0(x_0,y_0,z_0) is a given point and v=(a,b,c) is the given vector. The vector may also be in the format v=ai+bj+ck.
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