Finding vector C perpendicular to A with dot product constraint

[cdlegendary]

Homework Statement

You are given vectors vec A= 4.6i - 6.6j and vec B= - 3.0i + 7.2j. A third vector vec C lies in the xy-plane. Vector vec C is perpendicular to vector vec A and the scalar product of vec C with vec B is 18.0. (the i and j are hat values, they have a ^ over them)

Homework Equations

C * B = 18
C * B = |C|*|B|cos(x)
A * C = 0, because they are parallel

The Attempt at a Solution

I used the two equations
(Cx)(Bx)+(Cy)(By) = 18
(Ax)(Cx)+(Ay)(Cy) = 0

but could not reach a solution. I would greatly appreciate some guidance

 

[jegues]

(Cx)(Bx)+(Cy)(By) = 18
(Ax)(Cx)+(Ay)(Cy) = 0

You are given Bx, By, Ax, Ay, so you simply have 2 equations with 2 unknowns which you can solve for by a number of ways.