## anonymous 3 years ago Quick Question: Forces of magnitude 10 N and 8 N act in the direction shown. Write down in terms of theta, the component of the resultant of two forces: a) parallel to the force of magnitude 10N b) perpendicular to the force of magnitude 10N.

1. anonymous

2. marco26

Do summation of forces along the horizontal and vertical (x and y). Summation of forces along x will give you the answer to question A and y to B

3. anonymous

$$\vec F_1=8(-\cos \theta \hat a_x + \sin \theta \hat a_y)$$ $$\vec F_2=10 \hat a_x$$ adding gives $$\vec F=(10-8 \cos \theta) \hat a_x + 8 \sin \theta \hat a_y$$ so the component parallel is $$(10-8 \cos \theta)$$ and perpendicular is$$8 \sin \theta$$