Question

Vector A has a magnitude of 3.0 units and makes an angle of -90.0° with the positive x-axis Vector B has a magnitude of 4.0 units

and makes an angle of -120° with the positive x-axis. What is the magnitude of the vector sum A + B?

Answer choices:
(a) 1.0 units
(b) 6.8 units
(c) 7.0 units
(d) 5.0 units

Answer 1

Va = -3 j since vector A lies along the negative y-axis

Vb lies in the third quadrant (30 deg w.r.t. the negative y-axis)

Vbx = -4* sin 30 = - 2

Vby = -4 * cos 30 = -3.46

Vb = -2 i - 3.46 j

V = -3 j + (-2 i - 3.46 j) = -2 i - 6.46 j

V = (2^2 + 6.46^2)^1/2 = 6.76 magnitude of sum

(b) is correct