I want help on these questions, please?

MAT 241 Sample E... x X -/1 IVIA 1 241 MAT241 Sample Exam 1: 1. A force F = 3i + 5j + 10k moves an object along the line segment from (1, 0, 2) to (5, 3, 8). Find the work done if the distance is measured in meters and the force in Newtons. 2. Find parametric equations for the tangent line to the curve with the given parametric equations x = t2 + 1, y = 4Vt, z = elf-, at the point, (2, 4, 1). 3. Find an equation of the plane through (3, -1, 1), (4, 0, 2) and (6, 3, 1). 4. Determine if the planes x + y - z = 1 and 2x - 3y + 4z = 5 are parallel, perpendicular, or neither. If neither, find the angle between these planes to the nearest degree. 5. Evaluate the limit lim etz - 2 it - sin(t) - k - 2t 6. Find a vector function that represents the curve of intersection of the cylinder x2 + yz = 4 and the surface, z = xy. 7. Find the length of the curve r(t) = sin' (t) i + cos3(t) j + sin?(t) k on the interval, 0 S t S nt/2. 8. For the curve C defined by r(t) = ecos(t) i + etsin(t) j + 2k, find the following. (Simplify your answers as much as possible as you go.) a) The unit tangent vector. b) The unit normal vector. c) The curvature. 9. Find the position vector of a particle that has acceleration a(t) = eli + 2tj + (t + 1)k and an initial velocity of v(0) = i + k and an initial position of r (0) = 2i + j + k. O