# Determine values of m&n such that vector v(m-2, m+n, -2m+n) & w(2,4,-6) have same direction.

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Given that the two vectors are in the same direction does not necessary mean they have the same magnitude.

So suppose v=kw. we obtain:

m-2=2k

m+n=4k

-2m+n=-6k

Now we need to solve the system of equations:

If we substitue m=2+2k in the other two equations we obtain:

2+2k+n=4k and -2(2+2k)+n=-6k

Using the distubitive property and rearranging the terms we obtain:

n-4k=-2

n+2k=4

Subtracting the two equations we get:

-6k=-6 thus k=1.

So we can conclude that `m-2=2->m=4`

`m+n=4 -> n=4-4=0`

To confirm we use the third component `-2m+n=-2*4+0=-8!=-6`

Thus this problem does not have a solution.

It is given that these vectors are in same direction.

So we take O(0,0,0) as reference.

Then direction of VO = direction of WO

So m = 4 and n = 0

The answer is m=5 and n= 1, so the approach you took seems good, but the result is false.