To find the magnitude of a vector with three components, you can use the following formula:
Magnitude = √(x² + y² + z²)
Here, x, y, and z represent the three components of the vector. To illustrate this, let’s say you have a vector V with components (x, y, z) = (3, 4, 5). You would proceed by squaring each component:
- 3² = 9
- 4² = 16
- 5² = 25
Next, add these squares together:
9 + 16 + 25 = 50
Then, take the square root of the sum:
√50 ≈ 7.07
Thus, the magnitude of the vector (3, 4, 5) is approximately 7.07. This measurement gives you an idea of the vector’s length in a three-dimensional space, which can be very useful in various fields like physics and engineering.