MAT 141 - 3 Rev '23 1) Vector U = has a terminal point at (2,-1) . Find the initial point. 2) If vector U = and vector V = , find 30 - 4V . Write your answer in the i, j, k notation. 3) Find the magnitude and direction of the vector V = 4) Find the angle between vector U = and vector V = 5) Show that x2 + y2 + z? = 14y - 6z represents a sphere and find its center and radius. 6) Solve the following systems of equations -x - 5y - 5z =2 -6x - 2y + 2z =-8 4x - 5y + 4z = 19 3x - 2y - 42 = 8 x +5y- Z=-20 6x - 2y - 6z = -18 7) The work, W, done by a force, F, in moving along a vector, D, is W = F. D Find the work done by the force F in moving an object from points P to Q. F = 10i+ 3 j P ( 2, 3 ) Q (6 , -2 ) 8) The nth term of an arithmetic sequence is given by an = a + ( n - 1 )d where a is the 1st term and d is the common difference. Find the 100th term of the sequence 11, 8, 5, 2, . . . . .9) The nth term of a geometric sequence is given by an = arn- where a is the 1st number in the sequence and r is the common ratio. If the first term is 3 and the 3rd term is 4/3 . Find the 5th term. 10) The partial sum of an Arithmetic Sum is given by Sn = n/2[2a + (n - 1)d]. Find the partial sum of the arithmetic sequence 1+ 5 + 9 +. . . . . . .+ 401 11) Find the rectangular coordinates for the point whose polar coordinates are a ) ( 2 , = ) 12) 10) Convert the following rectangular coordinates to polar coordinates a ) ( - 2 , 2 ) 13) Convert the following polar equation to rectangular coordinates r = 3 sin 0 Formulas you might need X = r cos 0 cos 0 = - U.V lullv) Y = r sin 0 ( x- h ) 2 + ( y-k ) 2 + ( 2-1) 2 = 12 12 = x2 + yz a = |v| cos 0 and b = |v| sin 0 tan 0 = y/x 1v1 = Vaz + 62 V = v = = ai + bj