Please use proper vector notation. Do not use hats on vectors. a) Find the curvature of the following vector valued function for any value of t: (2t² – 2, 3t – 1, 5 + t) - b) Find the curvature at t == 1.

Q: Example Determine the unit tangent vector for r(t) = (t,t³,t5) at the point P = (1,2,3).

A: The vector is: .To Do:We have to determine the unit tangent vector at the point P=(1, 2, 3).

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Q: Let F(t) = (1, ²,4) and P = (2, 10, 4). Consider the curve C parametrized by F(t). Compute a tangent…

A: The objective of the question is to find the tangent vector, unit tangent vector, and the tangent…

Q: 2. Let P be the point (-3, 5, 4). (b) Find the distance from the point P to the yz-plane. Find the…

A: Let P be the point .(a) To find the distance from point P to the yz-plane.(b) To find the distance…

Q: 5. Find the parametric equations of the line that passes through the point (0, 1, 4)and is…

A: Given two vectors, u=2, -5, 1v=-3, 1, 4 Also, given the point, P=0,1,4 The cross product of u and v…

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Q: 1 Write the parametric equations x = 1 + ½ 2, y = t − 2 as a vector function, and then plot the…

A: Step 1: Step 2: Step 3: Step 4:

Q: Let 7(t) (-t + 5, 3e , - 5 sin( – 3t)) Find the unit tangent vector T(t) at the point t =0 T(0) --…

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Q: Consider the following vector function. - (46, ½-12², 1²) r(t): (a) Find the unit tangent and unit…

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Q: Calculate the velocity and acceleration vectors, and speed for when t = Speed: 11. Velocity:…

A: To calculate the velocity and acceleration vectors, and speed for .