# How to find the magnitude of a vector with 3 components

The magnitude of a vector signifies the positive length of that particular vector.

## Answer: The magnitude of a 3-dimensional vector with 3 components v_{1} = (a_{1}, a_{2}, a_{3}) is given as √(a_{1}^{2} + a_{2}^{2} + a_{3}^{2}).

Let's look into the given steps

**Explanation:**

The magnitude of a vector signifies the positive length of a vector. It is denoted by |v|.

For a 2-dimensional vector v_{1} = (a_{1}, a_{2}) the magnitude is given by √(a_{1}^{2} + a_{2}^{2})

For a 3-dimensional vector v_{1} = (a_{1}, a_{2}, a_{3}) the magnitude is given by √(a_{1}^{2} + a_{2}^{2} + a_{3}^{2})

Let's look into few examples to understand this.

Example 1: Find the magnitude of the vector xi + yj +zk

Magnitude = √(x^{2} + y^{2} + z^{2})

Example 2: Find the magnitude of the vector 2i + 3j + 4k

Magnitude = √(2^{2} + 3^{2} + 4^{2})

= √(4 + 9 + 16)

= √29