Home
Back
3D Vector Magnitude Formula:
| From: | To: |
The magnitude of a 3D vector represents its length or size in three-dimensional space. It's calculated using the Pythagorean theorem extended to three dimensions, providing the distance from the origin to the point (x, y, z) in space.
The calculator uses the 3D vector magnitude formula:
Where:
Explanation: The formula extends the Pythagorean theorem to three dimensions, calculating the straight-line distance from the origin to the point defined by the vector components.
Details: Vector magnitude is fundamental in physics, engineering, computer graphics, and mathematics. It's used to determine force magnitudes, velocities, distances, and is essential in vector normalization and various mathematical operations.
Tips: Enter the x, y, and z components of your 3D vector. The calculator will compute the magnitude. All values can be positive, negative, or zero, representing the vector's direction in 3D space.
Q1: Can vector components be negative?
A: Yes, negative components indicate direction opposite to the positive axis direction. The magnitude is always positive as it represents length.
Q2: What if all components are zero?
A: If x, y, and z are all zero, the magnitude is zero, representing a null vector at the origin.
Q3: How is this different from 2D vector magnitude?
A: 2D vector magnitude uses \( \sqrt{x^2 + y^2} \), while 3D adds the z-component: \( \sqrt{x^2 + y^2 + z^2} \).
Q4: What units are used for the magnitude?
A: The magnitude has the same units as the vector components. If components are in meters, magnitude is in meters; if in newtons, magnitude is in newtons, etc.
Q5: Can this calculator handle very large or very small numbers?
A: Yes, the calculator can process a wide range of numerical values, though extremely large numbers may be limited by PHP's floating-point precision.