If a 700-Ib load is suspended by two chains as shown in the gure to the right. What is the magnitude of the force each chain must be able to support? W I 700 lb Let F1 and F2 denote the forces exerted by the chains on the load and let F3 be the downward force due to the weight of the load. Place the vectors in a standard coordinate system shown to the right. If the load is in equilibrium (so the chains and load are stationary), which of the following equations should stand? F1+F2F3=0 V F1+F2+F3=0 F1-F2+F3=0 -F1-F2+F3=0 The force each chain must be able to support is El (Type an exact answer.) 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.)View an example | All parts showing x A small plane is ying horizontally due east in calm air at 325 mi/hr when it is hit by a horizontal crosswind blowing northwest at 50 mi/hr and a 30 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. (I) 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. Let Va be the velocity of the plane in calm air. The velocity of the plane in calm air (325 milhr due east) is v8 = 325i. Let vW be the velocity ofthe horizontal crosswind. The crosswind blows in the direction of northwest at 50 milhr. Its component to the west is 50 cos 45 = 2545 (in the - i direction). Its component to the north is 50 sin 45 = 251/5 (in the] direction). Therefore, the crosswind may be expressed as Vw = - 254/Ei + 25j. Let v"I be the velocity of the updraft. The velocity of the updraft (30 milhr) is vu = 30k. Let v be the velocity of the plane with the wind. Find the sum of the vectors Va, va and vu to nd v. V Va +Vw +Vu 325i + ( 254fi +25j)+30k (325 zsy + zsj + 30k Find the magnitude of this velocity vector to determine the speed of the plane with the wind