vectors

Vectors

• Definition: A vector is a quantity that has both magnitude and direction.

• Representation: Vectors can be represented graphically by arrows; the length indicates magnitude, and the arrow points in the direction.

• Types of Vectors:

  • Position Vector: Describes the position of a point in space relative to an origin.

  • Displacement Vector: The change in position of an object, measured in a straight line from the initial to the final position.

  • Velocity Vector: Represents the speed and direction of an object's movement.

  • Force Vector: Indicates the extent and direction of a force applied to an object.

• Operations:

  • Addition: Vectors can be added graphically (tip-to-tail method) or mathematically using components.

  • Subtraction: Involves adding the opposite vector.

  • Dot Product: A scalar product derived from two vectors, useful for finding angles.

  • Cross Product: A vector product yielding a vector perpendicular to the plane of the two original vectors.