Find the unit tangent vector T and the curvature K for the following parameterized curve. t}: (or? cost,1[|I cos t:1'i sint}l The unit tangent vector is T = ---.l. [Type exact answers. using radicals as needed} Find the unit tangent vector T and the curvature * for the following parameterized curve. r(t) = (6cos *t,6 sin *t) for 0 Ets T =Use the alternative curvature formula k = laxv 1v/ 3 to find the curvature of the following parameterized curve. r(t) = (6 cost, 0, are shown below. Use the definitions to compute the unit binormal vector B and torsion t for r(t). T= N = + + The unit binormal vector is B = (Type exact answers, using radicals as needed.)Evaluate the following definite integral. (( cos 6t)i + ( sin 6t)j + (8t)k) dt O A. (( cos 6t)i + ( sin 6t)j + (8t)k) dt = i+ )j + ( ) k +c O B. (( cos 6t)i + ( sin 6t)j + (8t)k) dt = it + k O| #Let u(t) = 5ti+ (t- -7)j-9k and v(t)= eli+ Ge j- ek. Compute the derivative of the following function. u(t) . v(t) Select the correct choice below and fill in the answer box(es) to complete your choice. O A. The derivative is the vector-valued function K. O B. The derivative is the scalar functionThe curve r(t) = (f(t), g(t)) , where f and g are twice differentiable, has curvature defined by the formula [f'g" -f"g' K(1) = - 3/2 : where derivatives are taken with respect to t. Find the curvature function of the following ((F) 2 + (9') 2 ) curve. r(t) = (4 sin t,3 cost) (ellipse) KO=