Given vectors \"A\" = - 4.8i + 6.8j and \"B\" = 9.6i + 6.7j determine the vector

Question

Given vectors "A" = - 4.8i + 6.8j and "B" = 9.6i + 6.7j determine the vector "C" that lies in the planeperpendicular to "B" and whose dot product with "A" is 20.0. So far I have the two equations (1) 9.6x +6.7y = 0 and (2) - 4.8x + 7.8y = 20. I am trying to solve forand x any y by substitution but my results are wrong. The answer for vector "C" = -1.4i + 2j. Can you please show me the work for solvingto get the equation? I already have the answer(above) -Thanks So far I have the two equations (1) 9.6x +6.7y = 0 and (2) - 4.8x + 7.8y = 20. I am trying to solve forand x any y by substitution but my results are wrong. The answer for vector "C" = -1.4i + 2j. Can you please show me the work for solvingto get the equation? I already have the answer(above) -Thanks

Explanation / Answer

we know A .C = 20 let C = x i + y j then -4.8 x +6.8 y = 20   ---( 1) B .C = 0 9.6 x + 6.7 y = 0 ----( 2) 2 * eq ( 1 ) + eq ( 2 ) ==> 2(6.8 y) +6.7 y = 2(20)                                                                  y = 1.97 from eq ( 2) , 9.6x = -6.7 y                           x = -1.375 So, vector C = -1.375 i +1.97 j

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