Vector Subtraction Calculator with Angles

Vector Subtraction Methods:

\[ \vec{R} = \vec{A} - \vec{B} = (A_x - B_x)\hat{i} + (A_y - B_y)\hat{j} \] \[ R = \sqrt{(A_x - B_x)^2 + (A_y - B_y)^2} \] \[ \theta = \tan^{-1}\left(\frac{A_y - B_y}{A_x - B_x}\right) \]

Vector A Magnitude:

units

Vector A Angle:

degrees

Vector B Magnitude:

units

Vector B Angle:

degrees

Resultant Magnitude:

Resultant Angle:

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1. What is Vector Subtraction?

Vector subtraction is the process of finding the resultant vector when one vector is subtracted from another. It's equivalent to adding the negative of the second vector to the first vector.

2. How Does the Calculator Work?

The calculator uses component-wise subtraction:

\[ \vec{R} = \vec{A} - \vec{B} = (A_x - B_x)\hat{i} + (A_y - B_y)\hat{j} \]

Where:

\( \vec{A} \) — First vector with magnitude and angle
\( \vec{B} \) — Second vector with magnitude and angle
\( A_x, A_y \) — Components of vector A
\( B_x, B_y \) — Components of vector B
\( \vec{R} \) — Resultant vector

Explanation: The calculator first converts polar coordinates (magnitude and angle) to Cartesian coordinates, performs the subtraction, then converts back to polar form.

3. Importance of Vector Subtraction

Details: Vector subtraction is essential in physics and engineering for calculating relative motion, net forces, and differences in vector quantities.

4. Using the Calculator

Tips: Enter magnitudes (must be ≥0) and angles in degrees for both vectors. The calculator will compute the magnitude and angle of the resultant vector.

5. Frequently Asked Questions (FAQ)

Q1: Why use component method for vector subtraction?
A: The component method provides precise results by breaking vectors into x and y components before performing operations.

Q2: How is angle calculated for the resultant?
A: The angle is calculated using arctangent of (Ry/Rx), with quadrant determined by the signs of the components.

Q3: What's the difference between vector and scalar subtraction?
A: Vector subtraction considers both magnitude and direction, while scalar subtraction only considers magnitude.

Q4: Can I subtract more than two vectors?
A: Yes, by sequentially subtracting each vector or adding all components first then performing one subtraction.

Q5: What if my resultant angle is negative?
A: Negative angles can be converted to positive by adding 360°, as they represent the same direction.