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[The word scalar means representable by position on a line; having only magnitude.] On the other hand physical quantities such as displacement, velocity, force and acceleration require both a magnitude and a direction to completely describe them. Such quantities are called vectors.
Three numbers are needed to represent the magnitude and direction of a vector quantity in a three dimensional space. These quantities are called vector quantities. Vector quantities also satisfy two distinct operations, vector addition and multiplication of a vector by a scalar.
•Introduction and revision of elementary concepts, scalar product, vector product. •Triple products, multiple products, applications to geometry. •Differentiation and integration of vector functions of a single variable.
Scalar and Vector Quantities. You will learn: The principles of scalar and vector quantities. Mathematical combinations of vector quantities. Unit vectors. Scalar Quantities: • A . SCALAR is a quantity of physics that has MAGNITUDE only, however, direction is not associated with it. Magnitude – A numerical value with units.
Describe the difference between vector and scalar quantities. Identify the magnitude and direction of a vector. Explain the effect of multiplying a vector quantity by a scalar.
Scalar product is the magnitude of a multiplied by the projection of b onto a. Obviously if a is perpendicular to b then a:b = 0. Also a:a = jaj2. p. (since =0 ) Hence a = (a:a) 2.1.1 Properties of scalar product. i:i = j:j = k:k = 1 and i:j = j:k = k:i = 0.
INTRODUCING VECTORS. 1.1 Scalars. 1.2 Vectors. 1.3 Unit vectors. 1.4 Vector algebra. 1.5 Simple examples. 1.1 Scalars. A scalar is a quantity with magnitude but no direction, any mathematical entity that can be represented by a number. Examples: Mass, temperature, energy, charge ...
