Question 1201656
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If (-1,3,5) x (0,a,1) = (-2,1,-1), determine a
This is from my 'cross product' lesson under vectors. Thank you.
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<pre>
The cross-product works this way

  (-1,3,5) x (0,a,1) = det {{{(matrix(3,3, i,j,k, -1,3,5, 0,a,1))}}}


In the right side i, j, and k are the unit vectors along x-, y- and z-coordinate axis.


Let's consider x-component of the cross-product. 
According to the rules of calculating this determinant, we should cross it out the first line and first row 
in this matrix and calculate the determinant of the remaining 2x2-matrix

    det {{{(matrix(2,2, 3,5, a,1))}}} = 3*1 - 5*a = 3 - 5a.


It should be equal x-coordinate of the vector (-2,1,-1), which is -2.


It gives us this equation

    3 - 5a = -2.


It is easy to solve

    3 + 2 = 5a

      5   = 5a

      a   = 5/5 = 1.


<U>ANSWER</U>.  a = 1.
</pre>

Solved, with explanations.