How Do You Calculate the Components of Vector C?

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To calculate the components of vector C, which is perpendicular to vector A and has a scalar product of 16 with vector B, the dot product equations must be established. The dot product of vectors A and C must equal zero, indicating their perpendicularity, while the dot product of vectors B and C must equal 16. Setting up these equations allows for solving the unknown x and y components of vector C. The discussion emphasizes the importance of understanding dot products in vector calculations. Properly applying these principles will lead to the correct values for vector C's components.
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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?




I'm not sure wither to use a dot product to solve this or use the cross product. I haven't yet learned how to use the cross product of two vectors so I don't think its that. How would i go about solving this problem? I thought about setting vector B equal to 16 but that didn't work out to well. Can someone please help me? Thank you!
 
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Well you know that the dot product of a and c has to equal zero and the dot product of a and b has to equal 16. So set up your equations and solve for x and y.
 

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