# 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 = (a, b, c) is given as √(a^{2} + b^{2} + c^{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 = (a, b) the magnitude is given by √(a^{2} + b^{2}).

For a 3-dimensional vector, V = (a, b, c) the magnitude is given by √(a^{2} + b^{2} + c^{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

### Thus, the magnitude of a 3-dimensional vector V = (a, b, c) is given as √(a^{2} + b^{2} + c^{2}).

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