Geometric Methods for Adding Vectors: Are You Doing It Right?

  • Thread starter Qube
  • Start date
  • Tags
    Vectors
In summary: It's important to note that the two methods shown in the pictures are just two different ways to visually represent the same vector relationship. In summary, the two different ways of adding vectors are the parallelogram rule and flipping the direction of one vector and adding as usual.
  • #1
Qube
Gold Member
468
1
Represent the below vector relationship geometrically, illustrating two different ways of adding vectors.

Vector a - vector b = vector c.

I know the above relationship can also be expressed as:

Vector a + (-vector b) = vector c.

In other words, we flip the direction of vector b and add as usual.

Attached are two pictures of me adding two *arbitrary* vectors a and b (vectors a and b change in the two attached photos).

In the first picture, I use the parallelogram rule. In the second picture, I use another method to add the arbitrary vectors a and b.

Did I add the two vectors together correctly?
ImageUploadedByTapatalk1391299475.883452.jpg

ImageUploadedByTapatalk1391299487.617555.jpg
 
Physics news on Phys.org
  • #2
  • #3
Qube said:
Represent the below vector relationship geometrically, illustrating two different ways of adding vectors.

Vector a - vector b = vector c.

I know the above relationship can also be expressed as:

Vector a + (-vector b) = vector c.

In other words, we flip the direction of vector b and add as usual.

Attached are two pictures of me adding two *arbitrary* vectors a and b (vectors a and b change in the two attached photos).

In the first picture, I use the parallelogram rule. In the second picture, I use another method to add the arbitrary vectors a and b.

Did I add the two vectors together correctly?
Your problem statement has the "-" sign with vector b, but your drawing has the "-" sign on vector a instead. Other than that, you have the right idea.
 

What is the definition of a vector?

A vector is a quantity that has both magnitude (size) and direction. It can be represented by an arrow, with the length of the arrow representing the magnitude and the direction of the arrow representing the direction.

How do you add two vectors geometrically?

To add two vectors geometrically, you first place the tail of one vector at the head of the other vector. The sum of the two vectors is then represented by the vector from the tail of the first vector to the head of the second vector. This is also known as the "head-to-tail" method.

What is the difference between adding vectors algebraically and geometrically?

Adding vectors algebraically involves using mathematical operations such as addition and subtraction to determine the resultant vector. Geometric addition, on the other hand, involves using the graphical representation of vectors to determine the resultant vector.

How do you find the resultant vector using the parallelogram method?

The parallelogram method involves drawing the two vectors with their tails at the same point. Then, a parallelogram is drawn with the two vectors as adjacent sides. The diagonal of the parallelogram represents the resultant vector.

What is the importance of adding vectors geometrically in science?

Adding vectors geometrically is important in science because it allows us to determine the resultant of multiple forces acting on an object. This is essential in fields such as physics and engineering, where understanding the net force on an object is crucial in predicting its motion.

Similar threads

  • Introductory Physics Homework Help
Replies
14
Views
325
  • Introductory Physics Homework Help
Replies
7
Views
989
  • Introductory Physics Homework Help
Replies
1
Views
750
  • Introductory Physics Homework Help
Replies
8
Views
803
  • Introductory Physics Homework Help
Replies
13
Views
514
  • Linear and Abstract Algebra
Replies
9
Views
201
  • Introductory Physics Homework Help
Replies
4
Views
1K
Replies
2
Views
1K
  • Introductory Physics Homework Help
Replies
11
Views
2K
  • Linear and Abstract Algebra
Replies
9
Views
576
Back
Top