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" thatlies in the plane perpendicular 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. How can you get this answer? Given vectors "A" = - 4.8i + 6.8j and"B" = 9.6i + 6.7j determine the vector "C" thatlies in the plane perpendicular 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. How can you get this answer?

Explanation / Answer

Given : .          Vector A = - 4.8 i + 6.8 j .           Vector B  =   9.6 i + 6.7 j .           Let Vector C =   x i   + y j .     Vector - C lies perpendicular to B. .             B . C = 0 .      or   (9.6 i + 6.7 j) . (x i   + y j) = 0 .      or   9.6 x  + 6.7 y   = 0  -----------(1) . Similarly   For A : .            -4.8 x   + 6.8 y =  20  -----------(2) . Solving (1) and (2)   we get : .            x   = - 1.375    and   y = 1.970 .             Vectro C =   - 1.375 i   + 1.970 y .                                 ˜   - 1.4 i + 2.0 j . Hope this helps u!

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