A Vector is a quantity that has direction and magnitude but has no position. The representation of this quantity is done by an arrow. The direction of the vector is the same as that of the object and the length is proportional to the magnitude of the quantity or object. Since the vector has no position, there is no change in the vector if the length remains the same.
Representation Of Vectors:
The vector diagrams are used to represent the vectors. A vector is represented as an arrow in the scaled vector diagram. The arrows are pointed and represents the specific direction. The displacement vector is shown on the vector diagram and has the following characteristics.
The head and tail of the arrow, the head represents the direction of the vector
Listing of the scale
The direction and magnitude of the vector. Example: Direction is 30 degrees NorthEast, the direction is 50 m.
How To Represent The Direction Of Vectors
There are two ways to represent directions:
An angle is used to represent the direction of the vector and the ‘tail’ of the arrow is used as the reference point for the angle of rotation. Example 50 degrees North of West means that the Vector is pointed to the West and has a rotation of 50 degrees towards the North.
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The angle rotation is clockwise and is referred from the tail of the arrow due east. Example a vector of 30 degrees is moved in clockwise and is relative to east. The convention of using the vector due east and rotating clockwise is most commonly used.
Vector Magnitude Representation:
The magnitude of the vector is represented by the arrow length and is based on the scale chosen. Example: Scale 1cm = 5 miles if the length of the arrow is 5 cm then the total is 5cm x (5 miles/1 cm) = 25 miles.
Real-Life Examples Of Vectors:
Vector quantity cannot be described unless both direction and magnitude are known. Take the following example: A football is located outside on the field, to fetch it move 20 meters. For someone who is about to find the football, there is incomplete information as there is no mention of the direction in which to move. If the statement is tweaked and it says move 20 m from the center of the room at a direction of 50 degrees North then this shows the vector which is relative to the starting point.
Some properties of moving objects are also termed as vectors. Take the example of the rolling billiard ball on a table. The movement of the ball is the velocity vector, the direction in which the ball moves are the vector arrow direction and the speed of the ball represents the vector length.
Any object can be represented using Vectors, even a common phenomenon like wind can be represented by a vector as it has direction and magnitude. Example: Northeasterly wind blowing at a speed of 50kmph can be represented on the map at different locations by drawing vectors.