I need help with these questions

13. In the cross (or vector) product F = qu x B we know that 9 = 1 F = -337 + -127 + -45k = - 8.07 + 7.0) + 4.0k B = Bi + B, j + BK What then is B in unit-vector notation if By = By? 14 . Two vectors a and b have the components, in meters, a, = 3.80, a, = 1.78, b, = 1.39, by = 6.15. (a) Find the angle between the directions of a and b . There are two vectors in the xy plane that are perpendicular to a and have a magnitude of 3.04 m. One, vector c , has a positive x component and the other, vector d , a negative x component. What are (b) the x component and (c) the y component of c, and (d) the x component and (e) the y component of vector d ? 15. If B is added to A, the result is 5.67 + 1.36). If B is subtracted from A, the result is -4.07 + 6.2). What is the magnitude of A? 16. Here are three vectors in meters: d, = -6.507 + 2.307 + 1.20% d2 = - 2.007 - 4.00 ) + 2.00k d3 = 2.007 + 3.00) + 1.00% What results from (a) d , . (d2 + d3 ). (b) d . . (d2 x d). and d , x (d2 + d3) ((c). (d) and (e) for i. ] and & components respectively)? 17. A protester carries his sign of protest, starting from the origin of an xyz coordinate system, with the xy plane horizontal. He moves 30 m in the negative direction of the x axis, then 21 m along a perpendicular path to his left, and then 43 m up a water tower. In unit-vector notation, what is the displacement of the sign from start to end? ((a), (b) and (c) for x, y and z components respectively) (d) The sign then falls to the foot of the tower. What is the magnitude of the displacement of the sign from start to this new end? A dot product, a cross product. We have two vectors: 14. a = ari + ayj 6 = bri + byj. What is the ratio by/b, if (a) a . b = 0and (b)a x b = 0? 19 Jungle gym, dot products, unit vectors. A coordinate system is laid out along the bars of a large 3D jungle gym (the figure below). You start at the origin and then move according to the following instructions. The direction for each move is explicitly shown but the distance (in meters) you move in that direction must be determined by evaluating a dot product of the given vectors A and B. For example, the first move is 21 m in the -x direction. What is the magnitude dnet of your final displacement from the origin? (a) -x. A = 3.0i. B = 7.0i (b) - z, A = 2.0k. B = 3.0j (c) +y. A = 5.0j. B = 3.0j (d) +x. A = 7.0k. B = 2.0k (e) - z, A = 3.0i. B = 2.0i (f) - y. A = 3.0i. B = 7.0j Road rally. The figure below gives an incomplete map of a road rally. From the starting point (at the origin), you must use available roads ZO . to go through the following displacements: (1) a to checkpoint Able, magnitude 36 km, due east; (2) b to check - point Baker, due north; (3)