V=? ### Proving Zero Curvature of a Curve**Problem Statement:**Prove that the curve \( r(t) = \langle a + bt^p, ct^d, dt^e + ft^p \rangle \), where \( a, b, c, d, e, \) and \( f \) are real numbers and \( p \) is a positive integer, has zero curvature. Provide an explanation.**Question:**What must be shown to prove that \( r(t) \) has zero curvature?- **A.** It must be shown that the velocity, \( v \), and the acceleration, \( a \), are constant.- **B.** It must be shown that the magnitude of the cross product, \( |a \times v| \), is zero, or that the unit tangent vector, \( T \), is constant.- **C.** It must be shown that the cross product \( a \times v \) is constant.- **D.** It must be shown that the dot product, \( a \cdot v \), is zero, or that the acceleration, \( a \), is constant.**Solution Approach:**- Show that the magnitude of the cross product, \( |a \times v| \), is zero.**Steps:**1. **Find the Velocity \( v \):** Given the parametric equation \( r = \langle a + bt^p, ct^d, dt^e + ft^p \rangle \), differentiate with respect to \( t \) to obtain \( v \). This will involve calculating each component of the velocity vector.2. **Next Steps:** Calculate the necessary cross product and demonstrate that its magnitude is zero.**Note:**This will confirm that the curve has zero curvature, by showing \( |a \times v| \) = 0, thus aligning with option **B** above.**Diagrams:**No diagrams or graphs are provided in this problem for analysis. The solution primarily involves algebraic manipulation and vector calculus.

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Prove that the curve r(t) = (a + bt",c+ dt",e+ ft"), where a, b, c, d, e, and f are real numbers and p is a positive integer, has zero curvature. Give an explanation. ..... What must be shown to prove that r(t) has zero curvature? OA. It must be shown that the velocity, v, and the acceleration, a, are constant. B. It must be shown that the magnitude of the cross product, Ja xv, is zero, or that the unit tangent vector, T, is constant. O C. It must be shown that the cross product a xv is constant. O D. It must be shown that the dot product, a• v, is zero, or that the acceleration, a, is constant. In this problem, show that the magnitude of the cross product, Jaxv, is zero. To do so, first find the velocity,v. (a + btP.c+ dtP, ,e+ ftP) V =