![]() ![]() Practical Applications of Multiplication of Vectors with Scalars ![]() Suppose the number considered as a scalar is 3, then the vector if multiplied by this scalar yields a product vector which is the same as three times the initial vector. On multiplying vectors with this scalar, the product obtained is a scaled version of the initial vector. Let any arithmetic number which is purely unitless be taken as the scalar quantity. The force is given as: F = m x aIn the above equation, ‘a’ denotes the acceleration which is a vector quantity and ‘m’ denotes the mass of the object which is scalar.So, it is one of the examples in Physics for the multiplication of vectors with scalars. This force is actually a product of a vector with a scalar quantity as per Newton’s second law of linear motion. The work done is dependent on both magnitude and direction in which the force is applied on the object. The physical quantity force is a vector quantity. In this case, the product vector is a vector which represents a vector whose direction is the same as that of vector ‘a’ and the magnitude is equal to ¼ times that of the vector ‘a’ (because 0.25 represents ¼). Scalar Vector Multiplication Rules ExampleĬonsider a certain vector say vector ‘a’ is multiplied with a scalar whose magnitude is 0.25. The product vector has the direction same as that of the vector which is multiplied with the scalar and its magnitude is increased as many times as the product of the magnitudes of vector and scalar that are multiplied. The product obtained by multiplying vectors with scalars is a vector. the magnitude of vectors is multiplied with that of the scalar quantities. A scalar can never be multiplied by a vector.ĭuring the multiplication of vectors with scalars, the similar quantities are subjected to arithmetic multiplication. At the same time, the converse of this is not possible. However, a vector quantity can be multiplied by a scalar. Addition of a scalar to a vector quantity is highly impossible because of their differences in dimensions. ![]() ![]() Though vectors and scalars represent different varieties of physical quantities, at times it is necessary for both of them to interact. If a vector is multiplied by a scalar it means that the magnitude of a vector is multiplied by a number. Multiplying vectors can be done in two forms namely dot product and cross product. Vector multiplication is finding the product of any two vectors either as a scalar or as a vector. Vector multiplication rules is one of the easiest and most interesting concepts in Mathematics. Scalars are represented by straight line segments without any arrow heads whereas vectors are represented by straight lines with an arrow head one of the end points indicating the direction of the vector. A physical quantity that has both magnitude and direction is called a vector quantity. A scalar quantity is direction independent. A physical quantity that has only magnitude is called a scalar quantity. However, quantities such as hunger, love, depression, anger etc cannot be characterized as physical quantities because they cannot be measured manually. A physical quantity is that quantity that can be measured physically using a scientific device. Have you ever wondered what a vector is and what can be done with vectors? If so, the answers to all your questions regarding vectors can be fetched in this article. ![]()
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |