Calc 3 Extra Credit #1 Question 1

Question

Find the area of the parallelogram having vectors u = < 1,2,1> and v= <3,1,1> as adjacent sides.

Answer 1

The area can be figured from the length of u, the length of v and the dot product u•v

The coordinate system independent formula for the square of the area, A² , is

A² = |u| |v| { |u| |v| - u•v }

With |u| = sqrt(6) , |v| = sqrt(11) and u•v = 6

A² = sqrt(66) { sqrt(66) - 6 }

A² = 49.75 and A = 7..05