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Question 1: Given the vectors v = (3,2,1) , u = (0,1,–1) , and w = (–1, 1,0) , compute the following : a) The unit vector parallel to w b) The angle between v and w c) The vector projection of u on w d) The equation of the plane parallel to v and w through the origin e) The equation of the line parallel to v through (1,0,0). Does this line pass through the point (–5,–4,–2)? Question 2: Given the plane 2x – 2y + z = 4 and the point P1 (0,–1, 2) on it. Let v = (1,0,1) be a vector in component form. a) Let the initial point of v be P1 . Give the coordinates of its terminal point Q . b) Give the component form of a vector perpendicular to the plane. c) Let P2 be a point on the plane such that the vector P2 Q is perpendicular to the plane. What is P2 Q ? d) What are the coordinates of P2 ? (Hint: The point P2 is the intersection of the line through P2 and Q with the plane) Question 3: A sphere with radius 2 is centered at the origin. Find the parametric equation of the intersection of the tangent planes to the sphere at ( 1, –1, 0) and ( -1, 0, 1). Question 4: Find all the local maxima, minima, and saddle points of the function f(x,y) = 2 x 3 2 y 3 9 x 2 3 y 2 12 y . Question 1: A sphere with radius 2 is centered at the origin. Find the parametric equation of the intersection of the tangent planes to the sphere at ( 0, 0, 2 ) and ( -1, 0, 1). Question 1: Find all critical points of the function f ( x, y) ( x 2 y 2 )( x 1) and classify them.