# Proving Perpendicularity: Solving Vectors Question | Homework Help

• noahsdev
This helps tutors to see what you are having trouble with and allows them to give you specific guidance. In summary, the conversation is about proving that the sum of two linearly independent vectors with equal magnitude is perpendicular to their difference, using the relevant equation v1.v2 = 0. The solution involves understanding the definitions of linear independence and scalar product, and showing that the given statement holds for any two vectors u and v. The OP is asked to show their attempt at solving the problem.
noahsdev

## Homework Statement

If two linearly independent vectors are of equal magnitude, prove that their sum is perpendicular to their difference.

v1.v2 = 0

## The Attempt at a Solution

This question doesn't seem that hard but it's really confused me.
Help is appreciated, thanks.

Just write down the scalar product!

noahsdev said:

## Homework Statement

If two linearly independent vectors are of equal magnitude, prove that their sum is perpendicular to their difference.

## Homework Equations

v1.v2 = 0
This is a "relevant equation" only if you say what v1 and v2 are! In particular are you clear that v1 and v2 are NOT the "two linearly independent vectors" of the question? Call the two vectors u and v. Their sum is u+ v and their difference is u- v. So "their sum is perpendicular to their difference" means (u+ v).(u- v)= 0. What does the fact that they are linearly independent tell you?

## The Attempt at a Solution

This question doesn't seem that hard but it's really confused me.
Help is appreciated, thanks.

noahsdev, per Physics Forums rules, you must show what you have tried when you post a question.

## 1. What is a vector?

A vector is a mathematical quantity that has both magnitude (size/length) and direction. It is commonly represented by an arrow in a coordinate system.

## 2. How do you add vectors?

To add two vectors, you must add their components (magnitude and direction) separately. The resulting vector will have a magnitude equal to the sum of the magnitudes of the original vectors, and a direction determined by the angle between the two original vectors.

## 3. What is the difference between a scalar and a vector?

A scalar is a quantity that has only magnitude, while a vector has both magnitude and direction. Examples of scalars include temperature, time, and mass, while examples of vectors include displacement, velocity, and force.

## 4. Can vectors be negative?

Yes, vectors can have negative components. This indicates that the vector is pointing in the opposite direction of the positive component. For example, a vector with a negative x-component is pointing in the negative x-direction.

## 5. How are vectors used in real life?

Vectors have many practical applications in real life, such as in navigation and mapping, physics and engineering, and computer graphics. They are also used in sports, such as in calculating the trajectory of a baseball or the velocity of a moving object.

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