# A small discussion on Orthogonal Vector

Hello, friends how are you?

Our today’s topic is-

Contents

# Orthogonal Vector:

## Definition:

Basically, the vectors which are perpendicular to each other are called Orthogonal vectors.

We can also say that if the scalar product(or Dot product) is zero then those vectors are called Orthogonal Vectors.

For example, If OA and OB are two perpendicular vectors then OA.OB=0, i.e they are orthogonal.

## Examples:

Now let’s see some problems.

## Problems:

Q1. show that a={1;2} and b={2;-1} are Orthogonal.

Ans.

a.b =1.2+2.(-1)=0 (Proved)

Q2. Find the value of n if a = {1;-2;n} and b={-4;-2;-5} are orthpgonal.

Ans:

a.b=1.(-4)+(-2).(-2)+n.5=0

⇒ -4+4-5n=0

⇒ n=0.

So, we can solve these types of problems very easily.

If you have any question regarding today’s topic, then you can ask here through the comment, we will add that problem and solve that.

Also, read- Orthogonal Matrix.

Thank you.