Question 1154874
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The area of the parallelogram is the absolute value of this determinant comprised of the given vectors' components 


   det {{{(matrix(2,2,  2,3,  -5,7))}}} = 2*7 - 3*(-5) = 14 + 15 = 29.


So, the area of the parallelogram is 29 square units.


The length of the vector [2,3] is  {{{sqrt(2^2+3^2)}}} = {{{sqrt(4 + 9)}}} = {{{sqrt(13)}}}.


Hence, the height of the parallelogram drawn to this side  [2,3]  is  {{{29/sqrt(13)}}}.


The length of the vector [-5,7] is  {{{sqrt((-5)^2+7^2)}}} = {{{sqrt(25 + 49)}}} = {{{sqrt(74)}}}.


Hence, the height of the parallelogram drawn to this side  [-5,7]  is  {{{29/sqrt(74)}}}.
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Solved, answered, explained and calculated.