given that p=i+j-2k and q=2i-j+2k.find two vectors m and n satisfying that m is perpendicular to p,n is parallel to p and m+n=q
m•p = 0
n = h(i+j-2k)
a+b-2c = 0
a+h = 2
b+h = -1
c-2h = 2
This gives the result
m = 5/2 i - 1/2 j + k
n = -1/2 i - 1/2 j + k
I don't see a second solution, but maybe you can find one.