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A Vector in Physics is a quantity which can be completely described by both direction and magnitude. The representation of the vector is an arrow - the direction of the arrow is the same as that of the quantity and the length of the arrow is in proportion to the magnitude of the quantity. Vectors physics examples include displacement, acceleration, velocity and force.

Note: A vector does not have any specific position. As long as the length and direction is the same a vector is not altered if it is displaced parallelly.

Representing a vector
Vectors are represented using scaled vector diagrams. A vector diagram is represented as an arrow drawn to scale in a particular direction.

It should be noted that a vector diagram has the following characteristics

  • The scale must be specified so as to correctly determine the magnitude from the diagram
  • An arrow representing the vector is drawn in a specific direction.
  • In order to improve the readability of the diagram, the magnitude and the direction of the vector are clearly labelled.
  • In order to represent the direction of the vector, we typically refer to the angle of rotation of the vector with the tail as the base point and east as the base direction.

Vectors and Direction | Image source: physicsclassroom.com

Vector physics examples
Displacement
Displacement is the movement of an object from its position. Displacement is a vector that represents the difference in position between two points. Its units are meters in a specified direction.

Velocity
Velocity is speed in a particular direction. Velocity is a vector as it represents the rate of change of displacement. Its units are meters per second is a specified direction.

Acceleration
Acceleration is defined as the rate of change of velocity. Since velocity is a vector, acceleration is also a vector quantity. The unit of acceleration is meter per second squared in a specified direction.

Force
Force causes change in the position of the object. It has both magnitude and direction and therefore it is a vector. The unit of force is newton is a specified direction.

Vector physics problems
A variety of operations can be performed on vectors such as addition, subtraction etc. You must keep in mind the directions of the vectors while performing these operations.

Addition of vectors
Two vectors can be added together. The sum is called the resultant vector. To add two vectors in a plane translate one of the vectors so that the endpoint of one vector coincides with the starting point of the second vector.

Addition of Vectors | Image source: philschatz.com

The resultant sum of the vectors is the starting point of the first vector and the endpoint of the second vector. As can be seen in the above diagram the resultant sum vector R is equal to A vector plus B vector

Subtraction of vectors
Vector subtraction can be performed in a similar method as addition of vectors. For eg: if we want to subtract vector B from vector A that is in order to carry out the operation A - B we must first flip the vector B.

Subtraction of Vectors | Image source: philschatz.com

The flipped vector B now has the same magnitude but the opposite direction of the original vector B. We can now proceed to add vector A and the flipped vector B in the same manner as addition of vectors to get the resultant vector R.

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