1. What is a Vector?

A vector is a mathematical object that has both magnitude (length) and direction. Vectors are commonly used in physics, engineering, and computer graphics to represent quantities like force, velocity, or position.

2. How to Calculate Vector Magnitude

The magnitude (length) of a vector is calculated using the formula:

Where:

• \( x \) — X component of the vector
• \( y \) — Y component of the vector
• \( z \) — Z component of the vector (0 for 2D vectors)

3. Understanding Unit Vectors

A unit vector is a vector with a magnitude of 1 that points in the same direction as the original vector. It's calculated by dividing each component by the vector's magnitude.

4. Using the Calculator

Instructions: Enter the x and y components of your vector. For 3D vectors, include the z component. The calculator will compute the magnitude and unit vector.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between a vector and a scalar?
A: A vector has both magnitude and direction, while a scalar has only magnitude (like temperature or mass).

Q2: How do I represent a vector graphically?
A: Vectors are drawn as arrows where the length represents magnitude and the arrow points in the direction of the vector.

Q3: What are unit vectors used for?
A: Unit vectors are often used to indicate direction without regard to magnitude, or as basis vectors in coordinate systems.

Q4: Can I calculate angles between vectors with this?
A: While this calculator doesn't directly compute angles, you can use the dot product formula with the unit vectors to find angles between vectors.

Q5: What if my vector has zero magnitude?
A: The zero vector has no direction, so it cannot be normalized to a unit vector (division by zero).