Please do 1 1. The equation x² + y² + z² 8x + 2y + 6z + 1 = 0 represents a sphere. Use the given equation to answerthe following questions.(a) Rewrite the equation in the form (x-a)² + (y - b)² + (z - c)² = R².(b) Identify the center and radius of the sphere.(c) Determine the curve in which the sphere intersects the yz-plane or explain why it is not possible.2. Let u = (3, 2, x) and v= (2x, 4, x).(a) Find all possible values of x that make u and v orthogonal.(b) Find proj, v.(c) Use the cross product to determine if there are any values of x that make u and v parallel.3. Determine if the following statements are True or False. Justify your answer with a proof or a counterex-ample.(a) If u v = 0, then one of the vectors must be the zero vector.(b) If u xv = 0, then one of the vectors must be the zero vector.(c) If u v= 0 and u x v = 0, then one of the vectors must be the zero vector.

1. The equation x² + y² + 2² - 8x + 2y +62 + 1 = 0 represents a sphere. Use the given equation to answer the following questions. (a) Rewrite the equation in the form (x-a)2+(y - b)² + (z - c)² = R². (b) Identify the center and radius of the sphere. (c) Determine the curve in which the sphere intersects the yz-plane or explain why it is not possible.