Finding Unknowns in Vector Equations

[nickh89]

Homework Statement

If A= (5.00 -7.00 ) units, B= (-7.00 + 2.00 ) units, and C= (27.0 + 20.0 ) units, determine a and b such that aA+ bB + C = 0.

Homework Equations

What I did to try and figure this out was solve for a and got the result of
a = -bB - C/ A

The Attempt at a Solution

What I did to try and solve this equation was plug that in for a, and take all the magnitudes of the vectors that are stated above but when i proceeded to do that everything would just cancel out when attempting to solve for b at that point. Any help would be great thank you.

 

[Cyosis]

You can't divide vectors like that. Secondly i take it that A=(5.00 , -7.00) is what you meant right? The way you have written it now suggests A=-2.

Plugging the components of the vectors into the vector equation will give you two "normal" equations. Since you have two unknowns and two equations you can solve a and b.

$$\begin{align}<br /> &5a-7b+27=0<br /> \\<br /> &-7a+2b+20=0<br /> \end{align}$$

 

[nickh89]

yes it was A = (5i, -7j), and thank you very much for the help.