# Check If Vector is Constant: Explanation & Tutorial

• kthouz
In summary, The conversation is about checking if a vector is a constant vector and how to approach this problem. The person being asked for help requests for a clear definition of a constant vector and an example of the problem. They also ask for clarification on the given vectors and variable.
kthouz
Can someone explain me how check if a vector is a constant vector?

You have to define your terms. What is a constant vector, i.e. how is it defined?

You check if it is a vector, you check if it is constant. What more do you want? Perhaps if you gave an example of the typ of problem you are trying to do it would help.

've been two perpendicular vectors r and v. r=coswi + sinwj where w is a constant and i and j are unit vectors.
The problem is to show first that v is perpendicular to r and then show that r x v is a constant vector. (here x is the cross product)

Okay, so you are given r= cos(w)i+ sin(w)j. You are also "given" v? What is v? Showing that v is perpendicular to r (for whatever v you are given) should be easy. Just take the dot product. As for a constant vector, so far you haven't mentioned any variable! Are you sure it wasn't r= cos(wt)i+ sin(wt)j where t is the independent variable?

It's really very difficult to help you if you don't tell use precisely what the problem is!

## What does it mean for a vector to be constant?

A vector is considered constant if all of its elements have the same value. In other words, the magnitude and direction of the vector remain unchanged.

## How can I check if a vector is constant?

To check if a vector is constant, you can compare all of its elements to each other. If they are all equal, then the vector is constant. Alternatively, you can also calculate the magnitude and direction of the vector and see if they remain unchanged.

## Why is it important to know if a vector is constant?

Knowing if a vector is constant is important in many scientific and mathematical applications. It allows us to simplify calculations and make predictions about the vector's behavior over time. It also helps us understand the concept of vector addition and subtraction.

## Can a vector be constant in one direction but not in another?

Yes, a vector can be constant in one direction but not in another. For example, a vector with a constant magnitude but changing direction is not considered constant. On the other hand, a vector with constant magnitude and direction in one dimension but changing in another dimension is still considered constant.

## How does a constant vector differ from a changing vector?

A constant vector has the same magnitude and direction throughout its entire length, while a changing vector has varying values for its elements and may have different magnitudes and directions at different points. Additionally, constant vectors do not change over time, while changing vectors can have different values at different points in time.

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