# Finding the Magnitude of a Diplacement Vector

• Love_to_Learn
In summary, the conversation discusses finding the displacement vector for cavers who traveled 2.6 km westward, 3.9 km southward, and 25 meters upward. The formula for the magnitude of the vector is used to calculate the distance and the displacement vector is defined as r = -2600i -3900j + 25k. It is clarified that the displacement vector conveys both magnitude and direction. The conversation concludes with the understanding that there was confusion between the terms "vector with a displacement" and "displacement vector" but the correct term is the latter.
Love_to_Learn
1. Cavers spelunked 2.6 km westward, 3.9 southward, and 25 meters upward. What is their displacement vector?

## The Attempt at a Solution

- The formula for the magnitude of a vector which is

sqrt of [(3.6)^2+(2.9)^2+(0.025)^2] ≈4.623 km

Let the point P1 lie at (-2600, -3900, 25).

Then OP1 will be a line segement whos magnitude is denoted as follows

sqr[ (-2600)^2 + (-3900)^2 + (25)^2 ] = 4687.28m = 4.69km

Looks about right, assuming it's 3.9km southward.

EDIT: I failed to read the question, The displacement vector would simply be r = -2600i -3900j + 25k, where i, j, k are the unit vectors of x, y, and z.

2nd EDIT: I reread the title and if you're looking for the magnitude of that displacement vector it is indeed 4.69km, sorry for the confusion.

Last edited:
Alright, then I am not understanding how to find a displacement vector. I thought that the displacement of a vector was the same as its magnitude. How is finding the displacement of a vector somehow different than finding the magnitude of a vector?

The displacement vector conveys both magnitude and direction. You have the distance, does the problem want direction as well?

How is finding the displacement of a vector somehow different than finding the magnitude of a vector?

I think you are mixing up terms, its not a vector with a displacement, its a displacement vector, this is a vector that defines displacement of an object based on another parameter(usually time).

jegues said:
I think you are mixing up terms, its not a vector with a displacement, its a displacement vector, this is a vector that defines displacement of an object based on another parameter(usually time).

You were exactly correct. That is what I was doing. Thanks for the replies everyone.

## 1. What is a displacement vector?

A displacement vector is a mathematical representation of the distance and direction between two points. It is commonly used in physics and engineering to describe the movement of an object.

## 2. How do you find the magnitude of a displacement vector?

The magnitude of a displacement vector can be found by using the Pythagorean theorem, which states that the square of the hypotenuse (longest side) of a right triangle is equal to the sum of the squares of the other two sides. In this case, the magnitude is equal to the square root of the sum of the squares of the horizontal and vertical components of the vector.

## 3. What units are used to measure the magnitude of a displacement vector?

The magnitude of a displacement vector is typically measured in units of length, such as meters or feet, depending on the measurement system being used.

## 4. How is a displacement vector different from a distance vector?

A displacement vector describes the change in position of an object, while a distance vector simply represents the total distance traveled by the object. Displacement is a vector quantity, meaning it has both magnitude and direction, while distance is a scalar quantity, meaning it only has magnitude.

## 5. Can the magnitude of a displacement vector ever be negative?

No, the magnitude of a displacement vector is always positive. The negative sign in front of a displacement vector indicates the direction of the displacement, not the magnitude.

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