A vector in physics is a quantity that has both magnitude and direction. It is represented by an arrow with the length of the arrow indicating the magnitude and the direction of the arrow indicating the direction.
The magnitude of a vector is determined by using the Pythagorean theorem, which states that the square of the hypotenuse (longest side) of a right triangle is equal to the sum of the squares of the other two sides. In other words, the magnitude of a vector is the square root of the sum of the squares of its components.
No, two vectors with the same magnitude and direction cannot be added together. When adding vectors, both magnitude and direction must be taken into account, so two vectors with the same magnitude but different directions will result in a different vector.
A scalar is a quantity that has only magnitude, while a vector has both magnitude and direction. Examples of scalars include temperature, mass, and time, while examples of vectors include velocity, force, and displacement.
Vectors can be represented mathematically using vector notation, which includes a magnitude and a direction. This can be written as a column matrix with the magnitude in the first row and the direction in the second row, or as a single letter with an arrow on top, such as v →.