Lesson 6: Summary on Vectors and Types of Vectors
- Some physical quantities, like mass, speed, and distance, are fully described by their magnitudes and units alone, while others, such as force, velocity, and displacement, require both magnitude and direction for complete specification.
- These quantities are known as vectors. Vectors are graphically represented by arrows, where the arrow’s length corresponds to the magnitude, and the arrow’s tip indicates the direction.
- For instance, a displacement of 10 km may be depicted by a 1 cm long arrow in a diagram, whereas a 20 km displacement might be shown by a 2 cm long arrow.
- Similarly, in velocity diagrams, an arrow representing a velocity of 5 m/s might be 1 cm long, and a velocity of 40 m/s would be 8 cm long.
- Understanding vectors is crucial in various practical applications. For example, engineers study the size and direction of all forces on a dam to design structures that withstand these forces.
- When rowing a boat, the forces involved include the backward push on the water by the oars and the forward force exerted by the water on the boat, along with the boat’s weight and the upward force from the water. In a tug-of-war, the rope transfers the forces between the participants.
- Vectors can be categorized into different types based on their properties and relationships.
- Parallel vectors are those that point in the same direction, while
- antiparallel vectors have opposite directions.
- Equal vectors have the same magnitude and direction regardless of their positions in space.
- Collinear vectors lie along the same line or parallel lines, and
- co-planar vectors lie in the same plane or parallel planes.
- A zero vector has a magnitude of zero, with its starting and terminal points coinciding.
- Orthogonal vectors are perpendicular to each other, and a unit vector has a magnitude of one.
- The concept of the negative of a vector is also important; it is defined as a vector with the same magnitude but the opposite direction, represented as -A if the original vector is A.
- These classifications help in analyzing and solving various physical scenarios involving vectors.