2 Dimensional Vector Calculator

2D Vector Components:

\[ \vec{v} = \langle v_x, v_y \rangle \]

Vector Magnitude (|v|):

Vector Direction (θ):

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1. What is a 2D Vector?

A 2D vector is a mathematical object that has both magnitude and direction in two-dimensional space. It's typically represented as an ordered pair of numbers \(\langle v_x, v_y \rangle\) where \(v_x\) is the horizontal component and \(v_y\) is the vertical component.

2. How Does the Calculator Work?

The calculator uses the following formulas:

\[ \text{Magnitude} = |\vec{v}| = \sqrt{v_x^2 + v_y^2} \] \[ \text{Direction} = \theta = \arctan\left(\frac{v_y}{v_x}\right) \]

Where:

\( v_x \) — Horizontal component of the vector
\( v_y \) — Vertical component of the vector
\( \theta \) — Angle in degrees from the positive x-axis

Explanation: The magnitude represents the length of the vector, while the direction represents the angle it makes with the positive x-axis.

3. Importance of Vector Calculation

Details: Vector calculations are fundamental in physics, engineering, computer graphics, and many other fields. They help describe quantities that have both size and direction, such as force, velocity, or displacement.

4. Using the Calculator

Tips: Enter the x and y components of your vector. The calculator will compute the magnitude (length) and direction (angle) of the 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 (like velocity), while a scalar has only magnitude (like speed).

Q2: How is vector direction measured?
A: Direction is typically measured in degrees from the positive x-axis, with positive angles going counter-clockwise.

Q3: What does a negative component mean?
A: Negative x-component means pointing left, negative y-component means pointing down (in standard coordinate system).

Q4: Can I use this for 3D vectors?
A: No, this calculator is specifically for 2D vectors. 3D vectors require an additional z-component.

Q5: What's the range of the angle output?
A: The angle ranges from -180° to +180°, with 0° along the positive x-axis.