Im confused on this problem explain please In the cross or v

In the cross (or vector) product F = q v x B we know that q=1 v =-2.0i + 2.0j + 7.0k What then is B in unit-vector notation if B, - 5

Solution

v = 2 i + 2 j + 7 k

F = 33 i + 9 j -12 k

q = 1

v XB =     i                           j                            k

   2    2    7            

            Bx                        By                         Bz

       = i[2Bz-7By]-j[2Bz-7Bx]+k[2By-2Bx]

q(vXB) = 1 {i[2Bz-7By]-j[2Bz-7Bx]+k[2By-2Bx]}

          = i[2Bz-7By]-j[2Bz-7Bx]+k[2By-2Bx]

We know F = q(vXB)

33 i + 9 j -12 k = i[2Bz-7By]-j[2Bz-7Bx]+k[2By-2Bx]

Compare this equation you get ,

2Bz-7By = 33          ---------( 1)

7Bx-2Bz = 9              -------------( 2)

2Bx-2By = 12           

Bx-By = 6    ------------( 3)

Eq(1)+eq(2) ==>7Bx -7By = 42

             Bx-By = 6       ------( 4)

Given Bx = -By

So, Bx+Bx = 6

           2Bx = 6

             Bx = 3

Substitute Bx in eq(2) you get ,

7(3)-2Bz = 9  

21 - 9 = 2Bz

      2Bz = 12

        Bz = 6

So, B = 3 i - 3 j + 6 K