1 Describe the given set of points with a single equation or with a pair of equations. The circle in which the plane through the point (5, 2, -6) perpendicular to the x-axis meets the sphere of radius 13 centered at the origin. x2 + y2 + z2 = 144 and y = 5 x2 + y 2 + z2 = 119 and y=5 x2 + y2 + z2 = 169 and z = 5 x2 + y2 + z2 = 169 and x = 5 Question 2 Find the length and direction (when defined) of u v. u = 2i + 2j - k, v = -i + k 3; 2/3i - 1/3j + 2/3k 3; 2/3i + 1/3j - 2/3 k 9; 2/9i - 1/9j + 2/9 k 9; 2/9i + 1/9j - 2/9 k Question 3 Find v u. v =( 1/ 3, 1/ 7 and u = (1/ 3 , -1/ 7 ) 1/3i - 1/7j 0 4/21 2/ 3 i Question 4 Describe the given set of points with a single equation or with a pair of equations. The set of points equidistant from the points (-7, 0, 0) and (6, 0, 0) y + z = -0.5 x > -7 and x < 6 x = -0.5 y + z = 0 and 7 -9 and z < 3 z = -6 Question 14 Find the length and direction (when defined) of u v. u = 4i + 2j + 8k, v = -i - 2j - 2k 180; 2 + 5/15 5/15 i+ 15/15 j k 180; 1/5i + 1/30k 6 5 ; 2 5/5 i- 5/5 k 6 5 ; 2 5/5 i+ 5/5 k Question 15 Give a geometric description of the set of points whose coordinates satisfy the given conditions. x2 + y2 + z2 > 1 All points on the surface of the cylinder with radius 1 All points outside the cylinder with radius 1 All points in space All points outside the sphere of radius 1 Question 16 Give a geometric description of the set of points whose coordinates satisfy the given conditions. (x - 3)2 + (y - 9)2 + (z - 3)2 < 1 All points outside the lower hemisphere centered at (3, 9, 3) No set of points satisfy the given relations. All points on the lower hemisphere centered at (3, 9, 3) All points within the lower hemisphere centered at (3, 9, 3) Question 17 Describe the given set of points with a single equation or with a pair of equations. The circle of radius 5 centered at the point (7, -4, 10) and lying in a plane perpendicular to the (y + 4)2 + (z - 10)2 = 25 and x = 7 (y/-4)2+ (z/10) 2+ 1 = 25 (y + 4)2 + (z - 10)2 = 25 and y+z=6 (y/-4)2 + (z/10)2 = 25 and x = 7 Question 18 Find the angle between u and v in radians. u = -2j and v = 3i - 3k 0.00 1.57 0.24 1.81 Question 19 Describe the given set of points with a single equation or with a pair of equations. The circle in which the plane through the point (1, 12, -4) perpendicular to the y-axis meets the sphere of radius 15 centered at the origin. x 2 + y2 + z2 = 144 and y = 12 x 2 + y2 + z2 = 225 and y = 12 x 2 + y2 + z2 = 63 and y = 12 x 2 + y2 + z2 = 81 and y = 12 Question 20 Find v u. v = 2i - 6j and u = -4 17 i + 5j (2 - 4 17 )i - 1j -30 17 + 8 -30 - 8 17 -30 17 i 8j