Understanding Vector Operations

Vectors represent quantities with both magnitude and direction, making them essential in physics and engineering for describing forces, velocities, and displacements.

How to Add/Subtract Vectors

Enter the x and y components of both vectors
Choose addition to find the resultant vector (A + B)
Choose subtraction to find the difference (A - B)
The result shows both component form and polar form (magnitude and angle)

Example Calculations

Adding (3,4) + (1,2): Resultant = (4,6) with magnitude 7.21 and angle 56.31°

Subtracting (5,3) - (2,1): Resultant = (3,2) with magnitude 3.61 and angle 33.69°

Common Vector Values

Vector Type	X Component	Y Component
Unit Vector (X)	1	0
Unit Vector (Y)	0	1
45° Vector	0.707	0.707

Tip: Always specify both magnitude and direction for complete vector description. Watch sign conventions in different quadrants.

Frequently Asked Questions

What is vector addition?

Vector addition combines two vectors by adding their corresponding components. The resultant vector represents the cumulative effect of both vectors.

How is vector subtraction different?

Vector subtraction finds the difference between components (A - B). This is equivalent to adding the negative of the second vector (A + (-B)).

Can I use this for 3D vectors?

This calculator handles 2D vectors only. For 3D vectors, you would need to include z-components in the calculations.

What units should I use?

Use consistent units for all components. The calculator doesn't require specific units - just ensure all inputs use the same measurement system.

Vector Addition Calculator

Result

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Vector Addition Calculator - Add and Subtract Vectors

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