SOLUTION: Find the lengths of both altitudes in the parallelogram determined by [2, 3] and [−5, 7].

Question 1154874: Find the lengths of both altitudes in the parallelogram determined by [2, 3] and [−5, 7].
Answer by ikleyn(52780) (Show Source): You can put this solution on YOUR website!
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The area of the parallelogram is the absolute value of this determinant comprised of the given vectors' components 


   det  = 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   =  = .


Hence, the height of the parallelogram drawn to this side  [2,3]  is  .


The length of the vector [-5,7] is   =  = .


Hence, the height of the parallelogram drawn to this side  [-5,7]  is  .

Solved, answered, explained and calculated.

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