Aship sets out to sail to a point 101 km due north. An unexpected storm blows the ship to a point 132 km due east of its starting point. (a) How far and (b) in what direction (as an angle from due east, where north of east is a positive angle) must it now sail to reach its original destination? (a) Number l Units V (b) Number n Units v wo vectors are given by a = ( 4.0 m )i - (3.0 m )7 + (1.0 m ) k and b = (- 1.0 m )i+ (1.0 m )7 + (4.0 m )k. In unit-vector notation, find (a) a + b, (b) a - b, and (c) a third vector c such that a - b + C = 0. N . > (a) Number i i k Units + + N . ) (b) Number i + c. > k Units + N . > (c) Number k Units + +(a) In unit-vector notation, what is the sum of a = (5.5 m )i + (2.0 m ) j and b = (- 12.0 m )i+ (7.3 m ) j. What are (b) the magnitude and (c) the direction of a + b (relative to i)? (a) Number i it i Units (b) Number i Units (c) Number UnitsThe two vectors 72' and j; in the gure have equal magnitudes of 13.2 m and the angles are 91 = 26 and 92 = 106. Find (a) the x component and (b) the y component of their vector sum 7'), (c) the magnitude of 7, and (d) the angle 7' makes with the positive direction of the x axis. (a) Number n Units V (b) Number n Units V (c) Number l Units V (d) Number n Units V An explorer is caught in a whiteout (in which the snowfall is so thick that the ground cannot be distinguished from the sky) while returning to base camp. He was supposed to travel due north for 5.1 km, but when the snow clears, he discovers that he actually traveled 8.3 km at 46 north of clue east. (3) How far and (b) in what direction (south of due west) must he new travel to reach base camp? (3) Number l Units V (b) Number n Units V