# Displacement Vectors: Understand x, y, z & i, j, k

• moondawg
In summary, displacement vectors are represented by the equation r=xi+yj+zk=<x,y,z>. The letters i, j, and k represent unit vectors in the x, y, and z directions respectively. They are used to indicate the magnitude of the component vectors in those directions. It is important to not confuse these unit vectors with the x, y, and z subscripts, as they represent different things.
moondawg

## Homework Statement

DISPLACEMENT VECTORS

## Homework Equations

r=xi+yj+zk=<x,y,z>

## The Attempt at a Solution

For all of the problems I am starting to do class we must use the equation above.
I do not understand why we use i,j,k and how they are similar to x,y,z and how to use them.
Please help! I was absent the day we learned this and it is a fast pace class and I am trying to understand this but can't seem to fully do so!

Its sort of the same thing, but not quite: i, j, and k are unit vectors in the x ,y, and z directions. Using x, y,and z subscripts, often imply magnitudes of the component vectors in those directions. So a vector 5i + 5j has a magnitiude of 5 units in the x direction and 5 units in the y direction. If you call the vector 5x + 5y, its easy to confuse yourself, as in your other post. So don't.

thankyou!

## What are displacement vectors?

Displacement vectors are mathematical representations of the distance and direction between two points. They are commonly used in physics and engineering to describe the motion of objects.

## What are the components of a displacement vector?

A displacement vector has three components: x, y, and z. These correspond to the three dimensions of space and represent the distance in each direction between the initial point and the final point.

## What is the difference between x, y, z and i, j, k in displacement vectors?

X, y, z are the Cartesian coordinates of a displacement vector, while i, j, k are the unit vectors in the x, y, z directions. They essentially serve the same purpose, but i, j, k are used to simplify calculations and equations.

## How do you calculate the magnitude of a displacement vector?

The magnitude of a displacement vector can be calculated using the Pythagorean theorem. The magnitude is the square root of the sum of the squares of the x, y, and z components.

## What is the importance of understanding displacement vectors?

Understanding displacement vectors is crucial in many fields, such as physics, engineering, and navigation. They allow us to accurately describe and predict the motion of objects in three-dimensional space, making them essential tools for solving complex problems.

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