Vector Quantities<\/h2>\n
Any quantity, such as velocity, momentum, or force, that has both magnitude and direction and for which vector addition is defined and meaningful; is treated as vector quantities.<\/p>\n
Note<\/strong> :<\/p>\n Quantities having magnitude and direction but not obeying the vector law of addition will not be treated as vectors.<\/p>\n For example, the rotations of a rigid body through finite angles have both magnitude & direction but do not satisfy the law of vector addition therefore not a vector.<\/p>\n A quantity, such as mass, length, time, density or energy, that has size or magnitude but does not involve the concept of direction is called scalar quantity.<\/p>\n To understand vectors mathematically we will first understand directed line segment.<\/p>\n Directed line Segment :<\/strong><\/p>\n Any given portion of a given straight line where the two end points are distinguished as Initial and Terminal is called a Directed Line Segment.<\/p>\n The directed line segment with initial point A and terminal point B is denoted by the symbol AB. The two end points of a directed line segment are not interchangeable and the directed line segments.<\/p>\n \\(\\overrightarrow{AB}\\) and \\(\\overrightarrow{BA}\\) must be thought of as different.<\/p>\n (a) Vector :<\/strong> (i) Length : <\/strong>The length of AB will be denoted by the symbol |AB|<\/p>\n Clearly, we have |AB| = |BA|<\/p>\n (ii) Support : <\/strong>The line of unlimited length of which a directed line segment is a part is called its line of support or simply the Support.<\/p>\n (iii) Sense : <\/strong>The sense of AB is from A to B and that of BA from B to A so that the sense of a directed line segment is from its initial to the terminal point.<\/p>\n (b) Scalar : <\/strong>Any real number is a scalar.<\/p>\n Two vectors are said to be equal if they have.<\/p>\n (a) the same length,<\/p>\n (b) the same or parallel supports and<\/p>\n (c) the same sense.<\/p>\n\n\nScalar Quantities<\/h2>\n
Mathematical Description of Vector & Scalar<\/h2>\n
![\"vector](\"https:\/\/i0.wp.com\/mathemerize.com\/wp-content\/uploads\/2021\/08\/vector-e1628799770837-300x251.png?resize=300%2C251&ssl=1\")
A directed line segment is called vector. Every directed line segment have three essential characteristics.<\/p>\nEquality of Two Vectors<\/h2>\n