Everything Science Grade 11

CHAPTER 11. VECTORS 11.8

�A

�B

�R

Figure 11.3: An example of two vectors being added to give a resultant

Each vector in Figure 11.3 can be broken down into one component in the x-direction (horizontal) and
one in the y-direction (vertical). These components are twovectors which when added give you the
original vector as the resultant. This is shown inFigure 11.4 where we can see that:

A� = A�x+A�y

B� = B�x+B�y

R� = R�x+R�y

But, R�x = A�x+B�x

and R�y = A�y+B�y

In summary, addition of the x components of the twooriginal vectors gives the x component of the
resultant. The same applies to the y components. So if we just added all the components together we
would get the same answer! This is another important property of vectors.

A�

A�x

A�x

�Ay �Ay

�B

B�x

B�x

�B

y

�B

y

�R

R�x

�R

y

Figure 11.4: Adding vectors using components.