two vectors, a and b in the figure have equal magnitudes of 10.0m and the angles

Question

two vectors, a and b in the figure have equal magnitudes of 10.0m and the angles are angle 1=30 degrees and angle 2= 105 degrees. Find the (a) x and (b) y components of their vector sum r, (c) the magnitude of r and (d) the angle r makes with the positive direction of the axis. Sorry, the equation editor won't add a diagram here, it won't work for some reason, but the tail of angle 2 is connected to the head of angle 1. thanks.                  two vectors, a and b in the figure have equal magnitudes of 10.0m and the angles are angle 1=30 degrees and angle 2= 105 degrees. Find the (a) x and (b) y components of their vector sum r, (c) the magnitude of r and (d) the angle r makes with the positive direction of the axis. Sorry, the equation editor won't add a diagram here, it won't work for some reason, but the tail of angle 2 is connected to the head of angle 1. thanks.                 

Explanation / Answer

vector a = 10 cos 30 i + 10 sin 30 j = 8.66 i + 5 j vector b = 10 cos 105 i + 10 sin 105 j = -2.588 i +9.659 j vector r = vector a + vector b = 6.072 i + 14.659 j x- component of r = 6.072 y-component of r = 14.659 magnitude of r = sqrt [ 6.072^2 +14.659 ^ 2] = 15.866 let r makes an angle theta with x - axis then tan (theta) = 14.659 / 6.072 theta = 67.5 degrees

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