I dont know how to solve these

What are (a) the x component and (b) the y component of a vector a in the xy plane if its direction is 249 counterclockwise from the positive direction of the x axis and its magnitude is 7.1 m? 2. The x component of vector A is -17.7 m and the y component is +50.4 m. (a) What is the magnitude of A? (b) What is the angle between the direction of A and the positive direction of x? 3. (a) In unit-vector notation, what is the sum of a = (3.7 m )i + (5.2 m )] and b = (- 17.0 m )i + (8.I m )7. What are (b) the magnitude and (c) the direction of a + b (relative to i)? 4 A car is driven east for a distance of 43 km, then north for 26 km, and then in a direction 31" east of north for 25 km. Determine (a) the magnitude of the car's total displacement from its starting point and (b) the angle (from east) of the car's total displacement measured from its starting direction. An explorer is caught in a whiteout (in which the snowfall is so thick that the ground cannot be distinguished from the sky) while 5. returning to base camp. He was supposed to travel due north for 5.4 km, but when the snow clears, he discovers that he actually traveled 8.3 km at 480 north of due east. (a) How far and (b) in what direction (south of due west) must he now travel to reach base camp? An ant, crazed by the Sun on a hot Texas afternoon, darts over an xy plane scratched in the dirt. The x and y components of four 6. consecutive darts are the following, all in centimeters: (27.0, 37.0), (b.. -66.0), (-25.0, cy), (-87.0, -62.0).The overall displacement of the four darts has the xy components (-120, -31.0).What are (a) b, and (b) cy? What are the (c) magnitude and (d) angle (counterclockwise from the positive direction of the x axis) of the overall displacement? 7. If B is added to C = 4.67 + 3.5), the result is a vector in the positive direction of the y axis, with a magnitude equal to that of C. What is the magnitude of B? 8. Oasis B is 6.0 km due east of oasis A. Starting from oasis A, a camel walks 24 km in a direction 15.0 south of east and then walks 32 km due north. If it is to then walk directly to B, (a) how far and (b) in what direction (relative to the positive x-axis within the range (-180%, 180*]) should it walk? What is the sum of the following four vectors in (a) unit-vector notation, and as (b) a magnitude and (c) an angle? Positive angles are counterclockwise from the positive direction of the x axis; negative angles are clockwise. A = (2.00 m )i+ (3.00 m )7 B = 4.00 m, at 65.0 C = (- 4.00 m )i - (6.00 m )7 D = 5.00 m, at -235 JO . Two vectors, 7 and 3' lie in the xy plane. Their magnitudes are 4.13 and 7.75 units, respectively, and their directions are 2910 and 31.09, respectively, as measured counterclockwise from the positive x axis. What are the values of (a) 7 . 3 and (b) |7 x |? For the following three vectors, what is 2 . C . (21 x B) ? A = 3.007 + 2.007 - 4.00% B = - 2.007 + 4.007 + 4.00k C = 7.007 - 9.007 2. Use the definition of scalar product, a . b = ab cos 0, and the fact that a . b = axb, + dyby + ab, to calculate the angle between the two vectors given by a = 5.0/ + 5.07 + 5.04 and b = 7.07 + 4.07 + 3.04