How to Calculate the Magnitude of a 3D Vector

What are the components of vector B?

Vector B has x, y, and z components of 9.2, 4.8, and 6.3 units, respectively.

What is the magnitude of vector B?

A. 12.1 units

Answer:

12.1 units

Explanation:

The magnitude of a 3D vector is calculated using the formula:

|V| = √(x² + y² + z²)

To calculate the magnitude of a 3D vector, such as vector B, you need to know its x, y, and z components. In this case, vector B has components of 9.2, 4.8, and 6.3 units along the x, y, and z directions, respectively.

The magnitude of a 3D vector represents the length of the vector in 3D space. It is calculated by taking the square root of the sum of the squares of its individual components. In the case of vector B:

x = 9.2, y = 4.8, z = 6.3

Therefore, the magnitude of vector B can be found as follows:

|V| = √(9.2² + 4.8² + 6.3²) = √(84.64 + 23.04 + 39.69) = √(147.37) ≈ 12.1 units

So, the magnitude of vector B is approximately 12.1 units.