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 √(a² + b² + c²).

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 √(a² + b²).

For a 3-dimensional vector, V = (a, b, c) the magnitude is given by √(a² + b² + c²).

Let's look into few examples to understand this.

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

Magnitude = √(x² + y² + z²).

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

Magnitude = √(2² + 3² + 4²)

= √(4 + 9 + 16)

= √29

Thus, the magnitude of a 3-dimensional vector V = (a, b, c) is given as √(a² + b² + c²).