Consider the vectors u = ( -9,0) and v = ( -3, -3) . Sketch the vectors, find the angle between the vectors, and compute the dot product using the definition u . v = |u| |v| cos 0. Sketch the vectors. Choose the correct graph below. A. O B. O C. 10 O D. 10- X X X - to X -to From the sketch, what is the angle between the vectors? 0 = (Type an exact answer, using it as needed.) What is the dot product? (-9,0) . ( -3, - 3) = (Simplify your answer.)Compute the dot product of the vectors u and v, and find the angle between the vectors. u= ( - 11,0,6) and v = (1,3,5) . . U . V= 19 (Type an integer or a simplified fraction.) Find the magnitude of the vectors. u = and v = (Type exact answers, using radicals as needed.)Define the points P( - 2,2) and Q(3, - 4). Carry out the following calculation. Find two vectors parallel to QP with length 2. The parallel vector of length 2 with the same direction is (Type exact answers, using radicals as needed.)The water in a river moves south at 5 km/hr. A motorboat is traveling due east at a speed of 39 km/hr relative to the water, determine the speed of the boat relative to the shore. . . . Let w represent the current; this means that | w| is the speed of the moving water and w points in the direction of the moving water. Assume that the vector vy gives the direction and speed of the boat relative the water, and the vector va gives the direction and speed of the boat relative to the shore. Place the vectors in a coordinate system. Choose the correct diagram below. A. O B. O C. OD. N N N W - -E W W - S V J W V W g w VW The speed of the boat relative to shore is approximately (Round to the nearest tenth as needed.) hr. km/hr. hr/km. km.A boat is towed with a force of 146 lb with a rope that makes an angle of 30 to the horizontal. Find the horizontal and vertical components of the force. Consider the figure (not to scale) to the right. It shows the force vector F along with its horizontal and vertical components, Fx and Fy, respectively. Which of the following formulas will correctly evaluate Fx and Fy? F O A. FX = |F| cot 0 and Fy = |F| tan 0 O B. FX = |F| sin 0 and Fy = |F| cos 0 C. FX = |F| cos 0 and Fy = |F| sin 0 O D. FX = |F | tan 0 and Fy = |F| cote The horizontal and vertical components of the force are |lb and Ib, respectively. (Type exact answers.) Consider the points P(0,0,72) and Q( - 9,9,0). a. Find PQ and state your answer in two forms: (a,b,c) and ai + bj + ck. b. Find the magnitude of PQ. c. Find two unit vectors parallel to PQ. a. Find PQ. PQ = ( - 9,9, -72) = (-9i+ (9 )j+ (-72) k b. Find the magnitude of PQ. The magnitude of PQ is (Type an exact answer, using radicals as needed.)A model airplane is flying horizontally due south at 40 mi/hr when it encounters a horizontal crosswind blowing west at 40 mi/hr and a downdraft blowing vertically downward at 20 mi/hr. a. Find the position vector that represents the velocity of the plane relative to the ground. b. Find the speed of the plane relative to the ground. a. Let the unit vectors i, j, and k point east, north, and upward, respectively. Begin by writing vectors describing the velocity of the plane relative to the air, the crosswind, and the downdraft. Find the vectors representing the velocity of the plane relative to the air v , the velocity of the horizontal crosswind v , and the velocity of the vertical downdraft vd. va=(0)i+(-40)j+(0)k vw=(4o)i+(0)j+(o)k vd=(o)i+(ojj+(2o)k The position vector of the velocity relative to the ground is ( 40 ) i + ( -40 )j+ ( -20 ) k. b. The speed of the plane relative to the ground is El m/s. mi/hr. km/hr. A small plane is flying horizontally due east in calm air at 275 mi/hr when it is hit by a horizontal crosswind blowing northwest at 40 mi/hr and a 10 mi/hr updraft. Find the resulting speed of the plane and describe with a sketch the approximate direction of the velocity relative to the ground. Let the unit vectors i, j, and k point east, north, and upward, respectively. Begin by writing vectors describing the velocity of the plane, the crosswind, and the updraft. What is the position vector that represents the velocity of the plane relative to the ground? The vector is ( )i + ()); + (10]k. (Type exact answers, using radicals as needed.)