Find the area of the parallelogram with vertices a(−3, 0), b(−1, 3), c(5, 2), and d(3, −1).

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ryanwilliamson6588 ryanwilliamson6588

16-04-2018
Mathematics

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Find the area of the parallelogram with vertices a(−3, 0), b(−1, 3), c(5, 2), and d(3, −1).

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mkryukova19 mkryukova19 · Answer 1 · 2018-04-16T14:09:58+02:00

|AD|=(3i-1j)-(-3i-0j)=3i-1j+3i+0j=6i-1j
|BA|=(-3i-0j)-(-1i+3j)=-3i-0j+1i-3j=-2i-3j

Area =|AD|x|BA|
= i j k
6 -1 0
-2 -3 0

= -1 0 i - 6 0 j + 6 -1 k
-3 0 -2 0 -2 -3

= 0 i - 0 j + (-18-2)k = -20 k

√(-20)² =20