Given u = (1-m)*i + 1+m)*j and v=(1+2m)*i+4j determine the vectors u and v whether u is perpendicular to v.

By definition, two vectors are perpendicular if the value
of their dot product is zero.

u*v = 0
(1)

[(1-m)*i+(1+m)*j]*[(1+2m)*i+4*j] = (1-m)*(1+2m) +
4*(1+m) (2)

We'll equate (1) and
(2):

(1-m)*(1+2m) + 4*(1+m) =
0

We'll remove the brackets:

1
+ 2m - m - 2m^2 + 4 + 4m = 0

We'll combine like
terms:

-2m^2 + 5m + 5 =
0

We'll multiply by -1:

2m^2 -
5m - 5 = 0

We'll apply quadratic
formula:

m1 =
[5+sqrt(25+40)]/4

m1 =
(5+sqrt65)/4

m2 =
(5-sqrt65)/4

The values of the parameter "m",
for the vector u to be perpendicular to the vector v, are: {(5-sqrt65)/4 ;
(5+sqrt65)/4}.