Vector Subtraction Calculator Magnitude And Angle

Vector Subtraction Formulas:

\[ R = A - B \] \[ R = \sqrt{R_x^2 + R_y^2} \] \[ \theta = \arctan\left(\frac{R_y}{R_x}\right) \]

Vector A X-component:

units

Vector A Y-component:

units

Vector B X-component:

units

Vector B Y-component:

units

Resultant Vector X-component:

Resultant Vector Y-component:

Magnitude:

Angle:

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What Is Vector Subtraction?

Vector subtraction is a fundamental operation in vector mathematics where we find the difference between two vectors. The resultant vector represents the relative position or displacement from one vector to another.

2. How Does The Calculator Work?

The calculator uses vector subtraction formulas:

\[ R = A - B \] \[ R = \sqrt{R_x^2 + R_y^2} \] \[ \theta = \arctan\left(\frac{R_y}{R_x}\right) \]

Where:

\( R \) — Resultant vector (A - B)
\( R_x \) — X-component of resultant vector (\( A_x - B_x \))
\( R_y \) — Y-component of resultant vector (\( A_y - B_y \))
\( \theta \) — Angle of resultant vector relative to positive x-axis

Explanation: The calculator subtracts corresponding components of vectors A and B, then calculates the magnitude using Pythagorean theorem and angle using arctangent function.

3. Importance Of Vector Subtraction

Details: Vector subtraction is crucial in physics, engineering, and computer graphics for calculating relative velocities, displacements, forces, and determining directions between points in space.

4. Using The Calculator

Tips: Enter the x and y components of both vectors A and B. The calculator will compute the resultant vector components, magnitude, and angle. All values can be positive, negative, or zero.

5. Frequently Asked Questions (FAQ)

Q1: What is the difference between vector subtraction and addition?
A: Vector subtraction A - B is equivalent to vector addition A + (-B), where -B is the vector with same magnitude but opposite direction as B.

Q2: How is the angle measured?
A: The angle is measured from the positive x-axis in counterclockwise direction, following standard mathematical convention.

Q3: What if both vector components are zero?
A: If both resultant components are zero, the magnitude will be zero and angle will be undefined (displayed as 0°).

Q4: Can I use this for 3D vectors?
A: This calculator is designed for 2D vectors. For 3D vectors, additional z-component calculations would be needed.

Q5: What are practical applications of vector subtraction?
A: Used in navigation (relative position), physics (relative velocity), computer graphics (object movement), and engineering (force analysis).