Can you provide a comprehensive review of physics vectors, including their properties, operations, and applications?

Vectors in physics are quantities that have both magnitude and direction. They are represented by arrows, with the length of the arrow indicating the magnitude and the direction indicating the direction. Vectors can be added or subtracted using the parallelogram rule or the head-to-tail method. They can also be multiplied by scalars to change their magnitude. Vectors are used in various applications in physics, such as in describing forces, velocities, and accelerations. Understanding vectors is essential for solving problems in mechanics, electromagnetism, and other branches of physics.