1. What is a Vector Calculator?

A Vector Calculator computes the magnitude and direction of a vector from its x and y components. Vectors are fundamental in physics, engineering, and mathematics for representing quantities with both size and direction.

2. How Does the Calculator Work?

The calculator uses these formulas:

Where:

• \( x \) — Horizontal component of the vector
• \( y \) — Vertical component of the vector

Explanation: The magnitude represents the length of the vector, while the direction (in degrees) indicates the angle from the positive x-axis.

3. Importance of Vector Calculations

Details: Vector calculations are essential in physics for analyzing forces, velocities, and accelerations. In engineering, they're used for structural analysis, electromagnetics, and computer graphics.

4. Using the Calculator

Tips: Enter the x and y components of your vector. The calculator will compute the magnitude (length) and direction (angle in degrees from the positive x-axis).

5. Frequently Asked Questions (FAQ)

Q1: What is a vector?
A: A vector is a quantity that has both magnitude (size) and direction, unlike a scalar which has only magnitude.

Q2: How is direction measured?
A: Direction is measured in degrees from the positive x-axis, with positive angles measured counterclockwise.

Q3: What if my vector is in 3D?
A: This calculator is for 2D vectors only. For 3D vectors, you would need to calculate magnitude using all three components and use different formulas for direction.

Q4: Why does the direction calculation need quadrant adjustment?
A: The arctan function only returns values between -90° and 90°, so we need to adjust based on the signs of x and y to get the correct quadrant.

Q5: Can vectors have negative components?
A: Yes, negative components indicate direction opposite to the positive axes. The magnitude is always positive.