Vector Magnitude C: Calculating Magnitude

[jack1234]

I am not sure how to do the following question(Attempts all failed):
Two vectors A and B are given by A = 4i + 8j and B = 6i – 2j. The scalar product of A and a third vector C is –16. The scalar product of B and C is +18. The z component of C is 0. What is the magnitude of C?

 

[hotcommodity]

Well, we know that A = <4, 8>, and B = < 6, -2>. If we dot A with a vector C and use the definition of the scalar product, we have:

$$A_xC_x + A_yC_y = -16$$

Doing the same for B we have:

$$B_xC_x + B_yC_y = 18$$

Now we have two equations and two unknowns. Does this help?

 

[jack1234]

Thanks a lot:) This is really far more simple than what I am thinking of !
The answer is 3.6.