A vector quantity has both magnitude and direction, while a scalar quantity only has magnitude. For example, velocity is a vector quantity, as it has both a numerical value (magnitude) and a direction (e.g. north, south, etc.), while speed is a scalar quantity as it only has a numerical value.
To add or subtract vectors, you must consider both their magnitude and direction. Vectors in the same direction can be added or subtracted by simply adding or subtracting their magnitudes. For vectors in different directions, you can use the Pythagorean theorem and trigonometric functions to find the resulting magnitude and direction.
Yes, you can have a negative vector. This typically indicates that the vector is pointing in the opposite direction of its positive counterpart. For example, a velocity of -5 m/s north means that the object is moving south at a speed of 5 m/s.
Vectors are commonly used in physics and engineering to describe the motion of objects, forces, and other physical quantities. Scalars are often used to describe simple measurements such as length, mass, and time. Both are also used in computer graphics and video games to represent movement and rotation.
Vectors can be represented visually using diagrams with arrows. The length of the arrow represents the magnitude of the vector, and the direction of the arrow represents the direction of the vector. The starting point of the arrow is typically placed at the origin of a coordinate system, and the end point is where the vector ends.