1. Jun 13, 2010

lrl4565

Alright, we have triangle abc with hypotenuse c. So, if you add vector a and vector b, the answer is vector c.

Now, according to the pythagorean theorem, this would not make sense. But the pythagorean theorem is DISTANCE. I am guessing that this phenomenon has something to do with using displacement?

2. Jun 13, 2010

Filip Larsen

Note, that the pythagorean theorem corresponds to the particular geometric situation where vector a and b are orthogonal on each other and in this case, the pythogorean theorem relates the length of the three vectors. For general vectors a and b, you need the law of cosine that includes the angle between a and b in order to related the length of a and b with the length of c.

3. Jun 13, 2010

lrl4565

My book says vector a + vector b = vector c. It uses (x,y) coordinates.

Vector a: (x1,y1)
Vector b: (x2,y2)
Vector c: (x1+x2, y1+y2)

Filip Larsen, what you just described gives me the magnitude of the displacement.

Am I measuring distance or displacement? Is the vector all about displacement?

4. Jun 13, 2010

Staff: Mentor

Displacement is only one example of a vector quantity. It's the first one that most physics textbooks introduce. There are many others: velocity, acceleration, force, momentum, angular momentum, electric field, magnetic field, ...

In your example, the total distance traveled would be the sum of the lengths (magnitudes) of the displacement vectors a and b:

$$d_{total} = \sqrt{x_1^2 + y_1^2} + \sqrt{x_2^2 + y_2^2}$$

The total displacement would be simply the vector c, which has magnitude

$$\sqrt{(x_1 + x_2)^2 + (y_1 + y_2)^2}$$

and a direction (angle) given by

$$\tan \theta = \frac{y_1 + y_2}{x_1 + x_2}$$

5. Jun 13, 2010

Naty1

6. Jun 13, 2010

lrl4565

7. Jun 13, 2010

diazona

What do you mean by "Euclidean vectors"?

8. Jun 13, 2010

lrl4565

Naty1's link is for Euclidean Vectors

9. Jun 13, 2010

diazona

Oh, silly me should've clicked on that.

From what I read in the article, it seems like a displacement vector is just one example of a Euclidean vector. Although it kind of depends on how you define "Euclidean vector" - there's a bit of ambiguity in the article, probably because different groups of people (e.g. physicists vs. mathematicians) have different definitions for the term.