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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 i

_{r}, with the same direction with OP( but starting at P.)

Another unit vector i

_{t}starts at P , but i

_{t}is perpendicular to vector i

_{r}. ( i

_{t}'s direction is toward north-west)

Express vector i

_{r}as a combination of unit vectors i and j.

Express vector i

_{t}as a combination of unit vectors i and j.

I found that i

_{r}= cos(θ ) i + sin(θ ) j

how to find i

_{t}? when I try to compute for i

_{t}, I found the same as i

_{r}, but I am not sure.

Please help

Thank you