- #1
hokhani
- 483
- 8
Why we can not define a vector as a quantity which has magnitude and direction? Why we define the vectors according to behavior of its components in rotated coordinate-frames?
A vector is a mathematical quantity that has both magnitude (size) and direction. It is represented by an arrow, with the length of the arrow representing its magnitude and the direction of the arrow representing its direction.
Magnitude refers to the size or amount of a vector, while direction refers to the orientation or angle of the vector. Both magnitude and direction are necessary to fully describe a vector.
A vector can be represented graphically as an arrow, with its length and direction indicating its magnitude and direction. It can also be represented mathematically using coordinates or components.
The magnitude and direction of a vector are independent of each other. This means that changing the direction of a vector does not affect its magnitude, and vice versa. However, the overall effect of a vector can change depending on its direction.
Some real-life examples of vectors include velocity (speed and direction of motion), force (magnitude and direction of push or pull), and displacement (distance and direction of movement). Vectors are also used in navigation, engineering, and physics to represent various quantities and phenomena.