Vectors are mathematical quantities that have both magnitude and direction. They are commonly represented by an arrow pointing in the direction of the vector, with the length of the arrow representing the magnitude.
Vectors can be represented by a set of coordinates or components, typically denoted by A = (ax, ay, az). The components indicate the magnitude of the vector in the x, y, and z directions, respectively.
The formula for finding the angle between two vectors A and B is cos θ = (A · B) / (|A| ⋅ |B|), where θ is the angle between the vectors, A · B is the dot product of A and B, and |A| and |B| are the magnitudes of A and B, respectively.
No, the angle between vectors cannot be negative. It is always measured in a counterclockwise direction from the first vector to the second vector, and therefore, it will always be between 0 and 180 degrees (or 0 and π radians).
The angle between vectors is commonly used in physics, engineering, and navigation to determine the direction and magnitude of forces, velocities, and displacements. It is also used in computer graphics and animation to create realistic movements and rotations.