VECTORS IN SPACE 1 point Find the direction cosines of the vector U = (2, -4, 4). COS O Cos B = COSY= COS O' = cos B= 3 COSY = Cold 3 O B COS Of = cos B = 5 COSY = COS O = Cos B = COSY= O c OD E. None of the aboveFind a vector perpendicular to the plane that passes through the points P(1, 4, 6), Q(-2,5, -1) and R(1, -1, 1). (-40, - 15, 15 (-20, - 8, 8) A OB (-35, - 4, 4) (-15, - 6, 6) O c OD E. None of the above\fFind the direction angles of the vector v = (2, -1, 3). a = cos a = cos- ), 8=0'),700' O A. OB. ( 1 8 =105 17=005 a = 00s' ), 8=005' ().7-006 O C. O D. O E. None of the above\fFind a unit vector u that has the same direction as the vector d = (-3, 3, - 2) 3 2 1 = 22 V22 V 22 22 V22 O A. OB. 3 -2 3 u = u = 26 V 26 V26 V26 V26 V26 O C. O D. E. None of the aboveFind the angle between A = (3, -2, 3) and B = (1, -3, -3). O A. O B. O C. O D. O E. None of the aboveDetermine the projection of A = (2, 1, -1) onto B = (1, 0, -2). -8 0, 5 0, O B. Co /N -2 3 OC. OD. O E. None of the aboveLet A = (2, 5, 3) and B = (-1, 2, 1). Find A x B. 117 - 3 - k -117 + 7 + k O A. O B. 1 + 57 -9% -7 - 57 + 9k O c. O D. O E. None of the aboveLet A = (2, 5, 3) and B = (-1, 2, 1). Find B x A. 117 - 3 - k -117 + 3 + k O A. (B. 1+ 53 - 9k -7 - 57 +9% O C. OD. E. None of the aboveFind the volume of the parallelepiped defined by the vectors u = (3, -1, 4), v = (2, 1, -2) and w = (5, 0, -1). O A. 14 O B. 15 O C. 16 O D. 17 O E. None of the aboveCYLINDRICAL SURFACES, SURFACES OF REVOLUTION AND QUADRIC SURFACES 1 point Find the distance (d) between the points (2, 3, -1) and (4, -1, 3). A. O B. O C. O D. O E. None of the aboveipoint Find the center and radius of the sphere x2 + 32 + 22 - 20 - 4y+ 82 + 17=0. center (1, 2, -4), radius 2 center (-1, -2, 4), radius 2 O A. O B. center (1, 2, -4), radius 4 center (-1, -2, 4), radius 4 O) C. O D. E. None of the above1 point Identify the surface of the equation (2 - 1)2 + +1 = 0. 9 4 A. Cylinder B. Ellipsoid C. Elliptic Paraboloid D. Hyperboloid of One Sheet E. None of the above 1 point Identify the surface of the equation TT 6 A. Cylinder B. Sphere C. Cone D. Elliptic Paraboloid O E. None of the above# 1 point Describe the surface of 42" - 4x2 - y = 4. A. Cone O B. Hyperboloid of one sheet C. Hyperboloid of two sheets D. CylinderConvert thc point (1, E, VIE) from cylindrical to spherical coordinates. O E. None of the above