Determine values of m&n such that vector v(m-2, m+n, -2m+n) & w(2,4,-6) have same direction.
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:
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:
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
`m-2-0 = 2-0`
`m = 4,`
`m+n-0 = 4-0`
`n = 4-4`
So m = 4 and n = 0