Vector Calculator with Graph

Vector 1 (X component):

Vector 1 (Y component):

Vector 2 (X component):

Vector 2 (Y component):

Operation:

Calculation Result:

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1. What is Vector Calculation?

Vectors are mathematical objects that have both magnitude and direction. This calculator helps visualize and perform operations on 2D vectors, making it easier to understand vector mathematics.

2. How Does the Calculator Work?

The calculator performs various vector operations:

\[ \text{Addition: } \vec{a} + \vec{b} = (a_x + b_x, a_y + b_y) \] \[ \text{Dot Product: } \vec{a} \cdot \vec{b} = a_x b_x + a_y b_y \] \[ \text{Cross Product: } \vec{a} \times \vec{b} = a_x b_y - a_y b_x \]

3. Vector Operations Explained

Vector Addition: Combines two vectors to produce a resultant vector.

Dot Product: Measures how much one vector extends in the direction of another.

Cross Product: In 2D, gives the signed area of the parallelogram formed by two vectors.

4. Using the Calculator

Tips: Enter the x and y components for both vectors, select an operation, and click Calculate. The graph will display the vectors visually.

5. Frequently Asked Questions (FAQ)

Q1: What are vectors used for?
A: Vectors are used in physics, engineering, computer graphics, and many other fields to represent quantities with direction.

Q2: How is vector magnitude calculated?
A: The magnitude of a vector (x,y) is √(x² + y²).

Q3: What does a negative dot product mean?
A: It means the vectors point in generally opposite directions (angle > 90°).

Q4: What does the cross product represent in 2D?
A: It gives the area of the parallelogram formed by the two vectors, with sign indicating orientation.

Q5: Can I use this for 3D vectors?
A: This calculator is for 2D vectors only. For 3D vectors, you would need a more advanced calculator.