The two vectors and in fig. 3-28 have equal magnitudes of 10.0 m and the angles are 30° and 105°. find the (a) x and (b) y components of their vector sum, (c) the magnitude of, and (d) the angle makes with the positive direction of the x axis.

You can just use basic trigonometry to solve for the x & y components.

vector a = 10cos (30) i + 10sin (30) j =

vector b is only slightly harder because the angle is relative to vector a, and not the positive x-axis. Anyway, this just makes vector b with an angle of 135deg to the positive x-axis.

vector b = 10cos (135) i + 10sin (135) j =

So now we can do the questions:

r = a + b

r =

(a) 5sqrt (3) - 5sqrt (2)

(b) 5+5sqrt (2)

(c)

|r| = sqrt ((5sqrt (3) - 5sqrt (2)) 2 + (5+5sqrt (2)) 2)

= 12.175

(d)

θ = tan-1 ((5+5sqrt (2)) / (5sqrt (3) - 5sqrt (2)))

θ = 82.5deg