Consider the three vectors shows in the figure. They have magnitudes |A| = 34.5,
ID: 1643497 • Letter: C
Question
Consider the three vectors shows in the figure. They have magnitudes |A| = 34.5, |B| = 10.5, and |C| = 33.2, and the labeled angles are theta_A = 40 degree, theta_B = 20 degree, and theta_C = 15 degree. Note that the figure shows the definitions of the angles, but the arrows in the figure may not be to scale. In what quadrant is the vector A+B+C? What is the magnitude of the vector A + B + C? What is the angle between the positive x-axis and the vector, measured clockwise in degrees? theta_1 = 236.53 -Use the formula for the angle between a vector and the positive x-axis, measured counterclockwise, in terms of the vector's components, but note that the required angle is measured clockwise. In what quadrant is the vector -A+2B+C? What is the magnitude of the vector -A + 2B + C? What is the angle between the negative x-axis and this vector, measured counterclockwise in degrees?Explanation / Answer
A = 34.5(cos40i + sin40j) = 26.4i + 22.2j
B = 10.5 ( - cos20i + sin20j) = -9.9i + 3.6j
C = 33.2 ( - sin15i - cos15j) = -8.6i - 32.1j
(A) A + B + C = 7.9i - 6.3j
that is 4th quadrant.
(B) magnitude = sqrt(7.9^2 + 6.3^2) = 10.1
(C) theta = tan^-1(6.3 / 7.9) = 38.6 deg
(D) A + 2B + C = -2i -2.7j
third quadrant
(E) magnitude = sqrt(2^2 + 2.7^2) = 3.36
(F) theta = tan^1-(2.7 / 2) = 53.5 deg