Unit Vector Notation Solution: Express Vector a1 & a2

[saber1357]

Homework Statement

Vector a1 + vector a2 = 5*vector a3
Vector a1 - vector 12 = 3*vector a3
Vector a3 = 2i + 2j (i and j are the vector components)
Express 1) vector a1 and 2) vector a2 in unit vector notation

Homework Equations

Vector R = Ax + Yx

The Attempt at a Solution

I took the first equation and replaces the a3 with 2i+2j, so vector a1 + vector a2 = 5(2i + 2j)
a1 + a2 = 10i + 10j
I solved for R and found direction, but I do'nt believe that helps at all. (R = sqr root of 200 and direction was 45 degrees).
From the first equation with addition, I could conclude that vector a1 could equal = 10i +0j and vector a2 could equal 0i + 10j. However, these values don't work for the second equation with the subtraction. Is there some sort of secret to this problem?

 

[D H]

Here is the trick. It is very simple and you will have many occasions to use it. Simply form the sum and difference of equations (1) and (2) any time you see a pair of equations of the form

$$\begin{align} x + y &= a\\x - y &= b\end{align}$$

Doing this yields

$$\begin{align*} 2x &= a+b\\2y &= a-b\end{align*}$$

This is much, much simpler than using the general simulataneous equations problem-solving techniques and these kind of paired equations occur all the time.

 

[saber1357]

Brilliant! Simply brilliant.
I love you.