If the vectors u and v are perpendicullar find m . u=mi+3j v=(m-2)*i-j

We'll put the vectors u and v in the standard
form:

u = xu*i + yu*j

v = xv*i
+ yv*j

Now, we'll write the constraint for 2 vectors to be
perpendicular:

the dot product of u and v has to be
zero,because the angle between u and v is 90 degrees and cos 90 =
0.

u*v = |u|*|v|*cos(u,v)

Now,
we'll identify xu,xv,yu,yv from the expressions of
vectors:

xu = m

xv =
(m-2)

yu = 3

yv =
-1

We'll calculate the product of vectors
u*v:

u*v = xu*xv + yu*yv

u*v =
m(m-2) + 3*(-1) (1)

But u*v = 0
(2)

We'll put (1) =
(2):

m(m-2) + 3*(-1) = 0

We'll
remove the brackets:

m^2 - 2m - 3 =
0

We'll apply the quadratic
formula:

m1 = [2 +
sqrt(4+12)]/2

m1 = (2 +
4)/2

m1 =
3

m2 =
(2-4)/2

m2 =
-1

Since it is not specified
if m has to be positive or negative, both values are
admissible.