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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.

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

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