Two points are given in polar coordinates by (r, 8) = (1.20 m, 50.0°) and (r, 0) = (4.00 m, -42.0°), respectively. What is the distance between them? m

m Let B = 5.05 m at 60.0°. C and A have equal magnitudes. The direction angle of Ĉ is larger than that of A by 25.0°. Let A · B = magnitude . . 29.1 m² and B C = 36.3 m². Find the magnitude (in m) and direction (in degrees) of A. direction

Given the vectors Ā = (-2î + j) m and B = (4î – j) m. The direction of the resultant vector R = Ả + B is O a. 8 = 180° O b.0 = 90° O c. 0 = 45° O d.0 = 0°

Each of the following vectors is given in terms of its x- and y-components. Find the magnitude of vector à and the angle it makes with respect to the positive x-axis, measured counterclockwise, when Ax = 4.00 and Ay = -4.00. A = Find the magnitude of vector B and the angle 0 it makes with respect to the positive x-axis, measured counterclockwise, when Bx = -3.00 and By = 3.00. B = 0A = C = ов = Find the magnitude of vector and the angle 0c it makes with respect to the positive x-axis, measured counterclockwise, when Cx = 0.00 and Cy = -2.00. 0c =

1. ANALYTICAL METHOD OF ADDING VECTORS Solve the same problem as PART 1 but this time analytically. START with the values below. DO NOT USE VALUES FROM PART 1. Suppose you first walk A = 12 m in a direction 20° west of north and then B= 20 m in a direction 40° south of west. Let the +x-axis coincide with the easterly direction and the +y-axis with the northerly direction. Note: In this problem, do not round values if you need to use them for calculations in subsequent parts. Rounding errors can propagate and can make your final answer lie outside the tolerance limit of 5% set for this problem. Keep all answers to 4 significant figures.

The x and y coordinates of point P are (-8.50 m, -7.00 m). What is the magnitude of point P?

The distance vector from point ? (2, −3, 1) and ?(1, 5, −3)a.   −?? + 8?? − 4??b.   ?? − 8?? + 4??c.   −0.11 ?? + 0.89?? − 0.44??d.   0.11 ?? − 0.89?? + 0.44??

1. Vector A is along the x-axis and vector B makes an angle with the z-axis. The magnitude of A - B is (a) A - B cos 0 (b) A - B sin 0 (c) √A²-B² (d) (A - B sin 0)2 + B² cos²0) (e) (A - B cos 0)² + B² sin² 0)

a. The two parallel lines (1, m) drawn below ate intersected by a third line. If angle 1 is 20 degrees, what are the values of the other angles 2, 3, 4, 5, 6, 7? 4 7/2 5 6 b. Given the geometry shown below, what is the value of the angle a? α 35° 00

9) Consider vector A = (7, 5) and vector B = (−3, −4). a) What is the direction and magnitude of vector A? b) What is the direction and magnitude of vector B? c) What is the direction and magnitude of vector C = A + B?