Sketching a parallelogram question

In summary, the problem asks to sketch a parallelogram in the xy-plane spanned by two vectors <2,1,0> and <-3,1,0>. The area has already been computed, so assistance is needed with the sketch. The request is for a quick explanation on how to sketch vectors in a 3D environment in the xy-plane. It is clarified that the sketch should only be in the xy-plane. The final question asks about the planes the two given points lie in and the plane the line connecting them must lie in.
  • #1
stau40
37
0

Homework Statement


Sketch the parallelogram spanned by <2,1,0> and <-3,1,0> in the xy-plane, and compute its area.


Homework Equations





The Attempt at a Solution


I have already computed the area, so I don't need help with that part. I do need help sketching the parallelogram though. I can't figure out how to sketch vectors in the 3D environment like it asks for. Can anyone provide a quick walk-thru as to how it's done? Thanks in advance!
 
Physics news on Phys.org
  • #2
It appears to ask for a sketch in the xy-plane, i.e. not in 3 dimensions
 
  • #3
How do I sketch three points <x,y,z> in an xy plane?
 
  • #4
What plane does the first point lie in? What plane does the second point lie in?

Thus, what plane must the line connecting these two point lie in?
 

FAQ: Sketching a parallelogram question

How do you sketch a parallelogram?

To sketch a parallelogram, you will need to follow these steps:

  • Start by drawing two parallel lines, which will serve as the sides of your parallelogram.
  • Next, draw two more lines connecting the ends of the parallel lines. These lines should be slanted and of equal length.
  • Make sure that the angles formed by the intersecting lines are equal.
  • You should now have a shape with two sets of parallel lines and four equal angles - this is a parallelogram.

What are the properties of a parallelogram?

A parallelogram has four sides, with opposite sides being parallel and equal in length. It also has four angles, with opposite angles being equal. Additionally, the diagonals of a parallelogram bisect each other and each diagonal divides the parallelogram into two congruent triangles.

How do you find the area of a parallelogram?

To find the area of a parallelogram, you can use the formula A = base x height. The base is one of the parallelogram's sides, and the height is the perpendicular distance between the base and its opposite side. You can also use the formula A = ½ x base x height, where base and height are the lengths of two adjacent sides.

Can a parallelogram have right angles?

Yes, a parallelogram can have right angles. In fact, a parallelogram with four right angles is a special type of parallelogram called a rectangle. However, not all parallelograms have right angles.

What is the difference between a parallelogram and a rectangle?

A rectangle is a type of parallelogram with four right angles. This means that all rectangles are parallelograms, but not all parallelograms are rectangles. Additionally, the opposite sides of a rectangle are equal in length, whereas in a parallelogram, all sides are equal in length.

Similar threads

Finding the area/volume for a transformed parallelogram/parallelepiped?
Replies
1
Views
3K
Area of a Parallelogram from 3D points
Replies
2
Views
10K
Norms question (parallelogram law)
Replies
1
Views
3K
ZPQM is a parallelogram, express Vector OZ in terms of u and v
Replies
6
Views
1K
I PDEs: Laplace's Equation over a Parallelogram
Replies
10
Views
3K
Sketching a periodic function and Fourier analysis
Replies
3
Views
2K
Which Vectors Correctly Determine the Interior Angle at B in a 3D Parallelogram?
Replies
2
Views
2K
Calculus III (help sketching graph)
Replies
1
Views
2K
Parallelogram Law of Vector Addition
Replies
2
Views
16K
What is the formula for finding the area of a parallelogram using vectors?
Replies
5
Views
1K

Hot Threads

Recent Insights

Back
Top