A vector is a mathematical object that has both magnitude (size) and direction. It is typically represented by an arrow, with the length of the arrow representing the magnitude and the direction of the arrow representing the direction of the vector.
To add vectors, you first need to make sure they are in the same dimension. Then, you can add the corresponding components of the vectors (e.g. add the x-components, add the y-components, etc.) to get the resulting vector.
A scalar is a quantity that has magnitude but no direction, while a vector has both magnitude and direction. Scalars can be added or multiplied together, but vectors can only be added or multiplied by other vectors.
The magnitude of a vector can be calculated using the Pythagorean theorem, where the magnitude is equal to the square root of the sum of the squares of the vector's components. For example, the magnitude of a 2D vector (x,y) would be √(x² + y²).
Vectors have many real-life applications, such as in navigation (e.g. using GPS coordinates), physics (e.g. calculating the force of a moving object), and computer graphics (e.g. creating 3D animations). They are also used in many other fields such as engineering, economics, and statistics.
