# Simple vector question

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• January 17th 2010, 11:45 PM
11rdc11
Simple vector question
Ok for some reason I'm not understanding this question or how to approach it

Express i and j in terms of a and b

a = 2i + 3j
b = i-j

Any help would be great, thanks.

The answer is

$i =\frac{1}{5}a +\frac{3}{5}b$

$j = \frac{1}{5}a -\frac{2}{5}b$
• January 17th 2010, 11:53 PM
Chris L T521
Quote:

Originally Posted by 11rdc11
Ok for some reason I'm not understanding this question or how to approach it

Express i and j in terms of a and b

a = 2i + 3j
b = i-j

Any help would be great, thanks.

The answer is

$i =\frac{1}{5}a +\frac{3}{5}b$

$j = \frac{1}{5}a -\frac{2}{5}b$

Note that (first eq) + 3*(second eq) will eliminate the j terms. This gives us $a+3b=5i$. Solving for i, we get $\frac{a}{5}+\frac{3b}{5}$.

Now substitute this into either equation to solve for j.

Can you take it from here?
• January 17th 2010, 11:57 PM
adkinsjr
Just treat the vectors as a system of equations.
• January 18th 2010, 12:16 AM
11rdc11
Quote:

Originally Posted by Chris L T521
Note that (first eq) + 3*(second eq) will eliminate the j terms. This gives us $a+3b=5i$. Solving for i, we get $\frac{a}{5}+\frac{3b}{5}$.

Now substitute this into either equation to solve for j.

Can you take it from here?

Wow I was completly overthinking that lol. Thanks again