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From: Albert on 13 Apr 2010 04:30
The vectors u and v are given by u = 7i + 8j and v = 2i - 4j (i and j
are unit vectors).

x(7i + 8j) + y(2i - 4j) = 44j
7xi + 8xj + 2yi - 4yj = 44j
(7x + 2y)i + (8x - 4y)j = 44j
(7x + 2y)i = (44 - 8x + 4y)j
i = j
7x + 2y = 44 - 8x + 4y
15x = 44 + 2y

What could I think about that would lead me to come up with another
equation?

TIA,
Albert
From: Albert on 13 Apr 2010 04:32
The aim is to find values for constants x and y.
From: William Elliot on 13 Apr 2010 04:55
On Tue, 13 Apr 2010, Albert wrote:

> The vectors u and v are given by u = 7i + 8j and v = 2i - 4j (i and j
> are unit vectors).
>
> x(7i + 8j) + y(2i - 4j) = 44j
> 7xi + 8xj + 2yi - 4yj = 44j
> (7x + 2y)i + (8x - 4y)j = 44j
> (7x + 2y)i = (44 - 8x + 4y)j
> i = j

No, you cannot claim i = j.

> 7x + 2y = 44 - 8x + 4y
> 15x = 44 + 2y
>
> What could I think about that would lead me to come up with another
> equation?
>
Lead you to where? If you want to solve for the scalars x and y,
then rewrite the equation in the form of
f(x,y)i + g(x,y)j = 44j

Then assuming that i and j are not only unit vectors but also
an independent set of vectors, you can claim
f(x,y) = 0, g(x,y) = 44

which will give you two linear equations in two unknowns
x and y which you can solve for, of course, x and y.

So juggle your first equation to find out what f(x,y) and g(x,y) are.

BTW, proof read before you post. It will save you time.

Note, no answer will be given to any post in which you clip out
the problem statement,
From: Greg Neill on 13 Apr 2010 07:32
Albert wrote:
> The vectors u and v are given by u = 7i + 8j and v = 2i - 4j (i and j
> are unit vectors).
>
> x(7i + 8j) + y(2i - 4j) = 44j
> 7xi + 8xj + 2yi - 4yj = 44j
> (7x + 2y)i + (8x - 4y)j = 44j
> (7x + 2y)i = (44 - 8x + 4y)j
> i = j
> 7x + 2y = 44 - 8x + 4y
> 15x = 44 + 2y
>
> What could I think about that would lead me to come up with another
> equation?

I think you've wandered off the path and into the
woods here.

First, recognize that unit vectors i and j cannot be
equal (except in magnitude) since they are usually taken
to be linearly independent by definition.

Second, you've already got your two equations in your
first line of math; they're simply mixed together.
You've only to separate them to proceed:

The i components: (7x + 2y)i = 0i

The j components: (8x - 4y)j = 44j

You should be able to take it from there.




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