# Ordering Vectors by Magnitude: BACDE

• huybinhs
In summary, the conversation discusses how to rank five given vectors in order of increasing magnitudes. The magnitude equation is mentioned and the attempt at solving the problem is shown, but there is confusion and a possible computation error. The method of finding the magnitudes is deemed correct.
huybinhs

## Homework Statement

Five vectors are listed below. Select them in order of increasing magnitudes, from shortest to longest. If B is smallest, then A, C, D, and finally E is the largest, enter BACDE (Note: If of equal length, then enter in the order listed.)
A) 23i-31j-17k
B) 36j+26k
C) 43j
D) 20i-34j-20k
E) 30i+30j

## Homework Equations

magnitude = sqrt (i^2 + j^2 + k^2)

## The Attempt at a Solution

I found:

A = 42.178

B= 44.407

C = 43

D = 44.226

E 42.426

I ranked: AECDB or even follow the order list: AECBD => It's showing wrong?

Could anyone explain what's going on? I'm really confused because I think I'm doing the right way!

Thanks!

As i see you squared the coordinates and took the root of their sum. Well that's the right way. probably some computation error. but the method is correct.

Anyone has different ideas?

## What is the concept of ordering vectors by magnitude?

The concept of ordering vectors by magnitude is to arrange a set of vectors in order from smallest to largest based on their magnitude, or length. This allows for a better understanding of the relative sizes and directions of the vectors in the set.

## How do you determine the magnitude of a vector?

The magnitude of a vector can be determined by using the Pythagorean theorem, which states that the square of the magnitude is equal to the sum of the squares of the vector's components. In other words, the magnitude is the square root of the sum of the squares of the vector's x, y, and z components.

## What is the difference between magnitude and direction of a vector?

The magnitude of a vector refers to its length, while the direction refers to the angle at which the vector is pointing. Both magnitude and direction are important in fully defining a vector in three-dimensional space.

## Why is it important to order vectors by magnitude?

Ordering vectors by magnitude allows for a better understanding of the relationships between vectors in a set. It also helps in visualizing the overall direction and magnitude of the set of vectors as a whole.

## Can vectors with the same magnitude have different directions?

Yes, vectors with the same magnitude can have different directions. This is because the magnitude and direction are separate components that define a vector. For example, two vectors with a magnitude of 5 can have different directions, such as one pointing north and the other pointing east.

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