Directions: You must show vour work to get credit. Write legibly and go step by step showing how your work leads to the final answer. A correct answer with no work shown or work that does not lead to the correct answer will receive no credit. A correct answer with some steps to get the answer omitted or with some incorrect steps may receive only partial credit. Also, an incorrect answer with correct work with minor mistakes will receive partial credit. Write all answers in simplest form. All work and answers must be hand written with pencil, pen, or I-pad. Graphs must be drawn by hand without the use of technology. 1) Find a scalar equation of a plane containing the point (2, 4, 5) and the line of intersection of the two planes x +2y +3z=4 and 2x -y +z=8. 2) Graph the surface y = 25 4x? z?, z = 0. Show some points and their coordinates in the graph. What is the name of this surface? 3) Find the point of intersection of the lines 7, (t) = (1 2t,3+,1 t) and ra(s) = (4+ 35,1 - 25,2 + 5). 4) Find the equation of the plane containing the point (2, 3, 3) and the line of intersection of the planes 2x + y 3z = 14 and -x + 5y + 2z = 16. 5) Find the unit tangent vector, the unit normal vector, and the curvature of #(e) = (t5t%62). 6) If a particle's position is given by 7(t) = (t,2cost,sint), find the velocity, acceleration, and speed of the particle when t = 0. Sketch the path of the particle. In the graph show the velocity and acceleration vectors when t = 0