Question

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.

Answer 1

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

Answer 2

\(\vec F_1=8(-\cos \theta \hat a_x + \sin \theta \hat a_y)\)
\(\vec F_2=10 \hat a_x \)
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\(8 \sin \theta\)