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Write the equation for the plane.The plane through the points P(-1, 3, -8) , Q(2, 3, 1) and R(1, -8, 31).

Solve the problem.A bullet is fired with a muzzle velocity of 1196 ft/sec from a gun aimed at an angle of 10° above the horizontal. Find the horizontal component of the velocity.

Perform the indicated operation.v = -5i + 2j – 3k and w = -4i – 3j + 2kFind | v | – | w | .   Type your answer in the given answer box.  You may need to use the equation editor found in the editing menu.  If the equation editor is not showing, click on the three vertical dots to expand the menu.  

Find projwv.v = 3i – 2j; w = -2i + j

Solve the problem. (Give your answer as a terminating decimal.)Find x so that the vectors v = i – xj and w = -5i + 2j are orthogonal.

Solve the problem.One rope pulls a barge directly east with a force of 44 N, and another rope pulls the barge directly north with a force of 81 N. Find the magnitude of the resultant force acting on the barge.

Perform the indicated operation.v = -2i – 6j – 3k and w = 2i + 3j + 5kFind  | v | – | w |. Type your answer in the given answer box.  You may need to use the equation editor found in the editing menu.  If the equation editor is not showing, click on the three vertical dots to expand the menu.  

Find a vector orthogonal to both v and u.v = -3i – 4j + k, u = -4i + 4j + 3k Type your answer in the given answer box.  You may need to use the equation editor found in the editing menu.  If the equation editor is not showing, click on the three vertical dots to expand the menu.  Be sure to use vector notation!  (Either use component form or i, j, k form.) 

Find the specified vector or scalar.u = -8i + j and v = 3i + j; Find  | u + v |. Type your answer in the given answer box.  You may need to use the equation editor found in the editing menu.  If the equation editor is not showing, click on the three vertical dots to expand the menu.  

Give the equation of the plane described below.The plane through the point (1, -4, -5) and parallel to the yz-plane Equation of the plane:  [xyz] = [number]