vector G is 40.3m long in a - 35.0 direction. Vector H is 63.3m long in a 270 direction. Find the direction of their vector sum

The resultant vector has a direction of - 69.1° or 290.9°.

Explanation:

The x component of the resultant vector is the sum of the x components of each individual vector.

x = 40.3 cos (-35.0) + 63.3 cos (270)

x = 33.0

Similarly, the y component of the resultant vector is the sum of the y components of each individual vector.

y = 40.3 sin (-35.0) + 63.3 sin (270)

y = - 86.4

The direction can be found with trigonometry:

atan (y / x)

atan (-86.4 / 33.0)

-69.1°

The resultant vector has a direction of - 69.1° or 290.9°.