The two vectors a Overscript right-arrow EndScripts and b Overscript right-arrow

Question

The two vectors a Overscript right-arrow EndScripts and b Overscript right-arrow EndScripts in the figure have equal magnitudes of 10.6 m and the angles are 1 = 26° and 2 = 103°. Find (a) the x component and (b) the y component of their vector sum r Overscript right-arrow EndScripts, (c) the magnitude of r Overscript right-arrow EndScripts, and (d) the angle r Overscript right-arrow EndScripts makes with the positive direction of the x axis.

https://edugen.wileyplus.com/edugen/courses/crs7165/art/qb/qu/c03/fig03_29.gif

Explanation / Answer

A = 10.6 (cos26 i + sin26 j)

A = 9.53 i + 4.65 j

and B = 10.6 ( cos(103 + 26) i + sin(103 + 26)j)

= - 6.67i + 8.24j

C = A + B

= 2.86i + 12.89 j

(A) Cx = 2.86 m

(B) cy = 12.89 m

(c) |C| = sqrt(cx^2 + Cy^2) = 13.2 m

(d) theta = tan^-1(12.89 / 2.86) = 77.5 deg

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