Please Help me to solve the Cal4 questions, it is due tonight

NAME: Have a high standard in your writing: Communicate clearly and show as much detail as you can in the work you know that requires it. Use the advice given in class often regarding this. Use proper notation. PROBLEM 14: In the space below, sketch the following points in the rst octant: (2,0, 0), (0, 3, 0), and (0, 0, 6). Note that these three points determine a plane. Depict this plane somehow in your sketch. PROBLEM 15: Let u be the vector from (2, 0, 0) to (0, 0, 6). Let v be the vector from (0, 0, 6) to (0, 3, 0). Then answer this question: Is the sum 11 + v the vector that carries a point from (2, 0, 0) to the point (0, 3, 0)? Why or why not? PROBLEM 16: Use the information in the previous problem to nd a vector normal to the plane. PROBLEM 17: Write the equation of the plane that you sketched on the previous page, the one containing intercepts (2, 0, O), (0, 3, 0), and (O, 0, 6). PROBLEM 18: Solve the equation you wrote for the plane for the variable 2. It is then in the form 2 _,f(x y); that is, z is a function of two variables. Restate the equation of the plane as this functlon f (x y) Compute the two first partial derivatives fr and f. Form the vector (12, f,, 1) and then go to the next problem. PROBLEM 19: Look back at where you found the vectors u and v. What is the dot product of u with the vector (fm, 1)? What is the dot product of v with the vector (aify, 1)? What is the vector (fx,f,, 1)? '1