The y component, Fy, is F times ey is this component

is equal to 10 times 0.866 or

8.66 Newtons.

And Fz, we can obviously tell, is going to be 0,

10 times 0 is 0.

And we can also write the vector force in this way.

In general, which is therefor,

equal to minus 5i plus 8.66j, in this example.

We can add vectors by simple adding them in a force polygon, head to tail.

So in this case, we have two vectors, V1 and V2.

And the vector, the sum of those two, is just V1 plus V2,

which we can do in this form here.

But, we can also do this by adding the component in the different directions.

So V1 is equal to iVx1 plus jy1,

where Vx1 and Vy1 are the x and

y components of the vector V1.

Similarly, V2 is iVx2 et cetera, so adding these 2 together,

we have V1 plus V2 is equal to iVx1 plus Vx2, et cetera.

In other words we can add the vectors by just adding their

components in the x and y and z directions separately.