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A measurable quantity that defines the laws of physics is known as physical quantity. The physical quantities are divided into two types:
A vector quantity can be represented graphically by the means of a straight line with an arrow as shown in the figure. The length of the straight line gives the magnitude of the vector and the arrow gives its direction. The starting point like 'O' is called tail and the ending point like 'A' is called head.
Notation of a vector
A vector quantity can be written as alphabet (small or capital) with arrow-head like
Example:\(\overrightarrow {OA}, \overrightarrow {OB},\overrightarrow {OC}\)
\(\vec a, \vec b,\vec c\)
\(\vec A, \vec B,\vec C\)
S.N | Scalar Quantities | Vector Quantities | |
1. | A physical quantity which has a magnitude but no direction is called scalar quantity. Example: length, mass, time, area, temperature etc. | 1. | A physical quantity which has both magnitude and direction is called vector quantity. Example: displacement, velocity, acceleration etc. |
2. | Scalar quantities change with the change in magnitude only. | 2. | Vector quantities change with the change in either magnitude or direction or both magnitude and direction. |
3. | Scalar quantities can be added or subtracted according to the ordinary rules of algebra. | 3. | Vector quantities cannot be added or subtracted according to the ordinary rules of algebra. |
4. | They are represented by ordinary letters. | 4. | They are represented by bold-faced letters or letters having an arrow over them e.g. \(\vec A\)is read as vector A. |
The necessary condition for a physical quantity to be a vector: Must have magnitude and direction.
Sufficient condition: To obey the vector law of addition.
A physical quantity which has a magnitude but no direction is called scalar quantity. Example: length, mass, time, area, etc.
A physical quantity which has both magnitude and direction is called vector quantity. Example: displacement, velocity, acceleration, force, etc.
A vector having magnitude 1 unit is known as a unit vector. The unit vector can be written as an alphabet with hat or cap
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Tekraj Timilsena
ohh so nice
Feb 02, 2017
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No Name
Is there any relationship between vector and scalar?
Jan 14, 2017
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