A scalar is a quantity that has only magnitude, while a vector has both magnitude and direction.
To add vectors, you must add their corresponding components. For example, to add two 2D vectors (x1, y1) and (x2, y2), you would add their x-components (x1 + x2) and their y-components (y1 + y2).
Yes, vectors can be multiplied by a scalar (a number). This is known as scalar multiplication and it results in a vector with the same direction but a different magnitude.
The magnitude (or length) of a vector can be found using the Pythagorean theorem. For a 2D vector (x, y), the magnitude is equal to the square root of (x^2 + y^2).
The dot product of two vectors is a scalar value that represents the magnitude of one vector multiplied by the projection of the other vector onto it. This can be calculated by multiplying the corresponding components of the vectors and then adding them together.