# Sketching a parallelogram question

• stau40
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.
stau40

## Homework Statement

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

## 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!

It appears to ask for a sketch in the xy-plane, i.e. not in 3 dimensions

How do I sketch three points <x,y,z> in an xy plane?

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?

## 1. 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.

## 2. 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.

## 3. 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.

## 4. 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.

## 5. 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.

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