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3D Vector Magnitude Formula:
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Vector magnitude represents the length or size of a vector in 3D 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 Cartesian coordinates.
The calculator uses the 3D vector magnitude formula:
Where:
Explanation: This 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 navigation. It's used to calculate forces, velocities, distances, and in 3D modeling to determine object sizes and distances between points.
Tips: Enter the x, y, and z components of your vector. The calculator will compute the magnitude. All values can be positive, negative, or zero, representing 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's the difference between magnitude and direction?
A: Magnitude is the size/length of the vector, while direction is where the vector points. Both are needed to fully describe a vector.
Q3: How is this different from 2D vector magnitude?
A: 2D magnitude uses √(x² + y²), while 3D adds the z-component: √(x² + y² + z²). The principle is the same but extended to an additional dimension.
Q4: What if my vector has zero magnitude?
A: A zero magnitude vector (when all components are zero) is called a null vector. It has no direction and represents a point at the origin.
Q5: How is vector magnitude used in physics?
A: In physics, vector magnitude calculates quantities like force strength, velocity speed, acceleration magnitude, and electric field strength.