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James Stewart

8 Edition

Chapter 12, Problem 27

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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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Official textbook answer

Video by Dylan Bates

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01:59

Find the area of the parallelogram with vertices $A(-3,0),$

$B(-1,3), C(5,2),$ and $D(3,-1)$

00:53

Find the area of the parallelogram with vertices $A(-2,1),$ $B(0,4), C(4,2),$ and $D(2,-1)$ .

07:07

Verify that the points are the vertices of a parallelogram, and find its area.

$$A(2,-3,1), B(6,5,-1), C(7,2,2), D(3,-6,4)$$

02:39

Find the area of the parallelogram whose vertices are $P_{1}, P_{2}, P_{3},$ and $P_{4}$.

$P_{1}=(-1,1,1) ; \quad P_{2}=(-1,2,2) ; \quad P_{3}=(-3,5,…

03:31

Find the area of the quadrilateral whose vertices, taken in order, are $(-4,-2),(-3,-5)$, $(3,-2)$ and $(2,3)$

03:30

Find the area of the parallelogram with vertices $P_{1}, P_{2}, P_{3},$ and $P_{4}$.

$P_{1}=(1,2,0), \quad P_{2}=(-2,3,4), \quad P_{3}=(0,-2,3)$

03:56

Find the area of the parallelogram with vertices $P_{1}, P_{2}, P_{3},$ and $P_{4}$.

$$

\begin{array}{l}

P_{1}=(-1,1,1), \quad P_{2}=(-1,2,2), \quad …

Transcript

Let’s try a parallelogram problem where we’re trying to find the area of a parallelogram defined by point A. At -30. We’ll call this one a B is negative 1 3 or happy See is that 5 to? We’ll call that C. & D. is at three negative one. We’ll call that D. In order to find the area of this parallelogram, we need to find vectors A. B. And A D. For example, that we can use to find the area of the entire parallelogram. So A. B. That’s just going to be b minus A. Or negative one minus negative three. That’ll be two, three minus zero. That’ll be three. And since we’ll be using the cross product here, the 3rd coordinate is just zero. Similarly, we can find the vector A. D. Which is just d minus a three minus negative three. His six -1 0 is -1. And once again our last coordinate will be zero. Since we’re trying to find the cross product A cross B. Let’s go ahead and put these vectors and our…