1. [40.097 Points] DETAILS LARCALCH 11.2.010. Find the coordinates of the point. The point is located six units in front of the yzplane, three units to the left of the xz-plane, and one unit below the xyplane. (x, V. 2) = ( ) Need Help? 2. [40.097 Points] DETAILS LARCALCH 11.2.0215. Find the distance dbetween the points {2, 2, 2} and (4, 5, 4}. d = Need Help? 3. [40.387 Points] DETAILS LARCALCH 11.2.029. Find the lengths of the sides of the triangle Iwith the indicated vertices, and determine whether the triangle is a right triangle, an isosceles triangle, or neither. All]; 0r 4L 50; 6r:l.]1' Cl. 4; -3] 0 right triangle 0 isosceles triangle 0 neither Need Help? 4. [-/0.387 Points] DETAILS LARCALC11 11.2.032.MI. Find the lengths of the sides of the triangle ABC with the indicated vertices. (Round your answer to three decimal places.) A(5, 0, 0) B(0, 9, 0) C(0, 0, -14) IABI = IACI = IBCI = Determine whether the triangle ABC is a right triangle, an isosceles triangle, or neither. O right triangle O isosceles triangle O neither Need Help? Read it Master It 5. [-/0.097 Points] DETAILS LARCALC11 11.2.033. Find the coordinates of the midpoint of the line segment joining the points. (6, 0, -7), (8, 2, 21) ( x , y, 2 ) = Need Help? Read it 6. [-/0.097 Points] DETAILS LARCALC11 11.2.038. Find the standard equation of the sphere with the given characteristics. Center: (-1, -6, 4) Radius: 9 Need Help? Read It7. [-/0.097 Points] DETAILS LARCALC11 11.2.039. Find the standard equation of the sphere with the given characteristics. Endpoints of a diameter: (2, 1, 5), (1, 7, -1) Need Help? Read It Watch It 8. [-/0.097 Points] DETAILS LARCALC11 11.2.042. Find the standard equation of the sphere with the given characteristics. Center: (-3, 0, 0), tangent to the yz-plane Need Help? Read It 9. [-/0.29 Points] DETAILS LARCALC11 11.2.044. Complete the square to write the equation of the sphere in standard form. x2 + yz + z" + 5x - 2y + 12z + 23 = 0 Find the center and radius. center (x,y,z) = ( radius Need Help? Read ItLARCALC11 11.2.049. DETAILS 10. [-/0.387 Points] The initial and terminal points of a vector v are given. Initial point: (-1, 7, 8) Terminal point: (8, 8, 9) (a) Sketch the directed line segment. 10 10 -10 -10 10 -10 -5 - 10 10 -5 5 - 10 -10 10 -5 5 5 X - -10 -5 5 X _ -10 10 X _ 10 O O O -10 -10 -10 X 10 O(b) Find the component form of the vector. v = (V1' V2: V3) = (c) Write the vector using standard unit vector notation. (d) Sketch the vector with its initial point at the origin. -10 10 -10 -10 10 -10 10 -10 -5 -10 5 5 5 10 5 -10 10 10 10 O O O 10 -10 5 -10 X10O Need Help? Read It 11. [-/0.097 Points] DETAILS LARCALC11 11.2.060. Find the vector z, given that u = , v = , and w = . z = 6u - 4v -_ Z Need Help? Read It 12. [-/0.097 Points] DETAILS LARCALC11 11.2.062. Find the vector z, given that u = (6, 0, 8), v = (1, 2, -4), and w = (4, 5, -3). 2u + v - w + 3z = 0 Z = Need Help? Read It 13. [-/0.097 Points] DETAILS LARCALC11 11.2.067. Use vectors to determine whether the points are collinear. (0, -2, -5), (14, 19, 2), (4, 4, -3) The points ---Select--- | collinear. Need Help? Read It Watch It13. [-/0.097 Points] DETAILS LARCALC11 11.2.067. Use vectors to determine whether the points are collinear. (0, -2, -5), (14, 19, 2), (4, 4, -3) The points ---Select--- |collinear. Need Help? Read It Watch It 14. [-/0.097 Points] DETAILS LARCALC11 11.2.072. Use vectors to show whether or not the points form the vertices of a parallelogram. (1, 1, 3), (3, -1, -2), (5, 2, -9), (3, 4, -4) O The given points form the vertices of a parallelogram. O The given points do not form the vertices of a parallelogram. Need Help? Read It Watch It 15. [-/0.097 Points] DETAILS LARCALC11 11.2.074. Find the magnitude of v. V = (-5, -4, -7) Jyll = Need Help? Read It 16. [-/0.096 Points] DETAILS LARCALC11 11.2.078. Find the magnitude of v. V = -3i + 3j + 8k Need Help? Read It17. [-/0.194 Points] DETAILS LARCALC11 11.2.079. Find a unit vector in the direction of v and in the direction opposite of v. V = (-3, -5, 5) (a) In the direction of v (b) In the direction opposite of v Need Help? Read It Watch It 18. [-/0.096 Points] DETAILS LARCALC11 11.2.083. Find the vector v with the given magnitude and the same direction as u. Magnitude Direction | | || = 18 U = (0, 5, 5) Need Help? Read It Watch It 19. [-/0.096 Points] DETAILS LARCALC11 11.2.086. Find the vector v with the given magnitude and the same direction as u. Magnitude Direction U = (-2, 8, 4) V = Need Help? Read It