Resolve each force acting on the support 2

Resolve each force acting on the support into its x and y components, and express each force as a Cartesian vector.

Image from: Hibbeler, R. C., S. C. Fan, Kai Beng. Yap, and Peter Schiavone. Statics: Mechanics for Engineers. Singapore: Pearson, 2013.

Solution:

Let us first draw each force separately on it’s own coordinate plane and break each vector into it’s x and y components. Each force is separately drawn below:

Carefully analyze each force and it’s components. Now, we can write each component using the i,j,k Cartesian coordinate system.

For force F_1 we see that it has two components, i and j which are both positive. So we can write F_1 as follows:

\vec{F_1} = \left\{800 \cos60^0(i)+800\sin 60^0(j)\right\}N

\vec{F_1} = \left\{400i+693j\right\}N

For force F_2 we see that it also has two components, but note that the i component is negative.

\vec{F_2} = \left\{600 \sin45^0(-i)+600\cos45^0(j)\right\}N

\vec{F_2} = \left\{-424i+424j\right\}N

Finally, for force F_3, note that the j component is negative.

\vec{F_3} = \left\{650(\frac{12}{13})(i)+650(\frac{5}{13})(-j)\right\}N

\vec{F_3} = \left\{600i-250j\right\}N

This question can be found in Engineering Mechanics: Statics (SI edition), 13th edition, chapter 2, question 2-39.