Find the area of the parallelogram with vertices A(-3,0) , B(-1,6) , C(8,5) and D(6,-1)

Reeves 2021-05-13 Answered
Find the area of the parallelogram with vertices A(-3,0) , B(-1,6) , C(8,5) and D(6,-1)

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Expert Answer

Cristiano Sears
Answered 2021-05-14 Author has 28671 answers

See the answer below:​​​image

Not exactly what you’re looking for?
Ask My Question
36
 
content_user
Answered 2021-09-29 Author has 11829 answers

Vertices are \(A(-3,0),\ B(-1,6),\ C(8,5)\) and \(D(6,-1)\)

So

\(\vec{AB}=<-1-(-3),6-0>=<2,6>\)

\(\vec{AD}=<6-(-3),-1-0>=<9,-1>\)

Hence area of parallelogram

\(=|\vec{AB}\times\vec{AD}|\)

\(\vec{AB}\times\vec{AD}=\begin{bmatrix}i&j&k\\2&6&0\\9&-1&0\end{bmatrix}\)

\(=i(0-0)+j(0-0)+k(-2-54)\)

\(=-56k\)

Hence

Area  \(=|\vec{AB}\times\vec{AD}|\)

\(=\sqrt{(-56)^2}=56\)

46

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Relevant Questions

asked 2021-06-11
Find the area of the parallelogram with vertices A(-3, 0), B(-1, 5), C(7, 4), and D(5, -1).
asked 2021-06-09
Change from rectangular to cylindrical coordinates. (Let \(r\geq0\) and \(0\leq\theta\leq2\pi\).)
a) \((-2, 2, 2)\)
b) \((-9,9\sqrt{3,6})\)
c) Use cylindrical coordinates.
Evaluate
\(\int\int\int_{E}xdV\)
where E is enclosed by the planes \(z=0\) and
\(z=x+y+10\)
and by the cylinders
\(x^{2}+y^{2}=16\) and \(x^{2}+y^{2}=36\)
d) Use cylindrical coordinates.
Find the volume of the solid that is enclosed by the cone
\(z=\sqrt{x^{2}+y^{2}}\)
and the sphere
\(x^{2}+y^{2}+z^{2}=8\).
asked 2021-06-04
Find an equation of the plane.
The plane through the points (4, 1, 4), (5, -8, 6), and (-4, -5, 1)
asked 2021-06-08

1) Find the area of the part of the plane
\(4x + 3y + z = 12\)
that lies in the first octant.
2) Use polar coordinates to find the volume of the given solid.
Bounded by the paraboloid \(z = 5 + 2x^2 + 2y^2\) and the plane z = 11 in the first octant

asked 2021-08-21

Given \(\displaystyle{u}=<{3},{5}>{\quad\text{and}\quad}{v}=<{6},{10}>\), find the magnitude of the vector and find the dot product.

asked 2021-08-16
Is it true that the equations r=8, \(\displaystyle{x}^{{2}}+{y}^{{2}}={64}\), and \(\displaystyle{x}={8}{\sin{{\left({3}{t}\right)}}},{y}={8}{\cos{{\left({3}{t}\right)}}}{\left({0}\le{t}\le{2}\pi\right)}\) all have the same graph.
...