I have a problem about vector coordinates. this is the problem:

We have a 2-dimension space [x(unit vector i) and y( unit vector j)].

I have a circle of center 0 (0,0) and a point P such that OP = r.

Vector OP and the x-axis have an angle of θ .

there is a unit vector

**ir**, with the same direction with OP( but starting at P.)

Another unit vector

**it**starts at P , but vector

**it**is perpendicular to vector

**ir**. (vector

**it**'s direction is toward north-west)

Express vector

**ir**as a combination of unit vectors i and j.

Express vector

**it**as a combination of unit vectors i and j.

I found that

**ir = cos(θ ) i + sin(θ ) j**

how to find it ? when I try to compute for vector

**it,**I found the same as vector

**ir**, but I am not sure.

Please help

Thank you