Question

Give a geometric description of the set of points whose coordinates satisfy the given conditions. 1) X-5-4 A) All points in the x-z plane B) The line through the point (5.0,-4) and parallel to the y-axis C) The line through the point (5. -4,0) and parallel to the z-axis D) The point (5.-4) Describe the given set of points with a single equation or with a pair of equations. 2) The plane perpendicular to the y-axis and passing through the point (4. -9,-4) A) X - 9+ z = 0 B) 4x - 42 -0 and y = -9 C) y = -9 D) X = 4 and 2 = -4 3) The circle of radius 4 centered at the point (7.-1.1) and lying in a plane perpendicular to the x-axis A) (y + 1)2 + (x - 1)2 - 16 and X = 7 B) (y + 1)2 + (z - 12 - 16 and y + 2 0 +1 = 16 --0- D) Oy = 16 and x7 Find the distance between points Pa and P2 P2P 4) P1(2,6,6) and P2(4,10,10) A) 14 B) 18 C) 6 D) 10 Find the center and radius of the sphere. 5) x2 + (y + 8)2 + (2-4)2 - 49 A) C(0,8,-4), a = 7 C) C(0, -8,4), a - 49 B) C(0,8.-4), a -49 D) C(O. -8,4), a = 7 Solve the problem 6) Find a formula for the distance from the point P(x, y, z) to the z-axis. A) 17+y B) x² + y² C) Vz2+y? D) x + y Find the indicated vector. 7) Let u -(-6, -7), v = (6.5). Find u + v. (TIA) (-1,-1) B)(-13, 11) C) (-12-12 is 0) (0.-2 8) Let u = (-5. -3). Find -7u. A) (35,21) B)(-35, 21) C)(-35, -21 D) (35.-21) D) (-27.64 9) Let u =(-1,5). V = (4.3). Find - 9u + Sv. A) (-36,56) B)(-23, -69 C) (41, -21) Express the vector in the form v = v1i+v21 +v3 k. 10) P1 P2 it P, is the point (6,-4,4) and P2 is the point (8. -7,0) A) = -21 - 3j 4 B) v = 21 - 3j - 4 C) -21 3j - 4 D) -21 + 3] + 4

Answer 1

a Given x = 5, Z =-4 Write the line equation, X-5 y-0_2-(-4) 0 P 0 Compare with the line *-* = "=Y1-2-31 and intercept fom. b (47.91:21)=(5:0:-4) and y-intercept (0.p.0) Therefore, the dr's of the line (0.p.) parallel to the y-axis. And it's represent a line passing through the point (5,0.-4) and parallel to the y-axis. Hence the correct option is B