Calculus and Vectors

20. Determine the angle between a@ = (5, 3, 0) and b =(-1,0,8) 21. The vertices of a quadrilateral are A = [0, 3,5],B = [-3,-1,17], = [4,-3,15] & D =[7,1,3]. Prove that ABCD is a parallelogram. o z+1 k-1 x=1 -2 22. Determine the value of & for which the direction vectors of the lines " = T x+3 Z _2 = I' y = 1 are perpendicular. and 33. Sketch the diagram that you would use to find the magnitude of the sum of @ and b if the angle between them is 67" and the magnitudes are 7 and 11 respectively. Ensure that all vectors are labelled. Also include the equilibrium vector in your diagram. ! 34. For the function whose graph is given below, find the following: a. llIP f(x)= b. lirg;f(x]: . 1in;1f(x]: d. lirrjl_f(x}: e. lirrjl_f(x}z f. limlf(x} - g Jf(@2)= h S(D=