Component problem. Please help!?

You are given vectors A= 4.7i - 7.0j and B= - 3.2i+ 6.9j . A third vector C lies in the xy-plane. Vector C is perpendicular to vector A and the scalar product of vector C with vector B is 16.0.





What is the x-component of vector C?





What is the y-component of vector C?

Component problem. Please help!?
C is perpendicular to A. Hence


A · C = 0


%26lt;=%26gt;


4.7·Cx - 7.0·Cy = 0


%26lt;=%26gt;


4.7·Cx = 7.0·Cy





e.g


Cx = 7.0


Cy = 4.7


Any multiple of these vector fulfills the condition above too. Thus the vector we look for is:


C = λ·(7.0i + 4.7j)





The dot product with vector B is 16.0


B · C = 16


%26lt;=%26gt;


-4.2·λ·7.0 + 6.9·λ·4.7 = 16.0


%26lt;=%26gt;


λ = 16.0/3.03


=%26gt;


C ≈ 36.96i + 24.81j

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