Suppose vector A=3i-2j, B= -i-4j and vector C are three vectors in xy plane with the property that vectors A+B-C. What is the unit vector along vector C?

Answer 1

Don't you mean that A + B = C ?

A + B - C is not a property. It is a vector that depends upon what C is.

A "unit vector along C" will depend upon how C is defined. It will be a combination of i and j. It is hard to believe they are really asking for that.

Answer 2

I bet Dr WLS is right and that - sign should be an = sign

making that assumption:
A + B = C = 2 i - 6 j
so
we need a unit vector in the C direction
Find magnitude of i - 3 j which is in C direction
sqrt (1^2 + 3^2) = sqrt (10)
so
(1/sqrt 10) i - (3/sqrt 10) j