Since vectors are graphical visualizations, addition and subtraction of vectors can be done graphically. One of the ways in which representing physical quantities as vectors makes analysis easier is the ease with which vectors may be added to one another. Ideas about magnitude and direction are introduced and examples of both vectors and scalars are given. The difference between Vectors and Scalars, Introduction and Basics: This video introduces the difference between scalars and vectors. Talking about the direction of these quantities has no meaning and so they cannot be expressed as vectors. Some examples of these are: mass, height, length, volume, and area. Scalars are used primarily to represent physical quantities for which a direction does not make sense. Scalars differ from vectors in that they do not have a direction. Typically this reference point is a set of coordinate axes like the x-y plane. In order to specify a direction, there must be something to which the direction is relative. Each of these quantities has both a magnitude (how far or how fast) and a direction. Physical concepts such as displacement, velocity, and acceleration are all examples of quantities that can be represented by vectors. The greater the magnitude, the longer the arrow. ![]() The two parts are its length which represents the magnitude and its direction with respect to some set of coordinate axes. In the geometric interpretation of a vector the vector is represented by an arrow. The magnitude of a vector is a number for comparing one vector to another. Vectors require both a magnitude and a direction. Vectors are usually represented by arrows with their length representing the magnitude and their direction represented by the direction the arrow points. Scalars can be thought of as numbers, whereas vectors must be thought of more like arrows pointing in a specific direction.Ī Vector: An example of a vector. In contrast, scalars require only the magnitude. Vectors require two pieces of information: the magnitude and direction. These two categories are typified by what information they require. Physical quantities can usually be placed into two categories, vectors and scalars. Distinguish the difference between the quantities scalars and vectors represent.Together, the two components and the vector form a right triangle. The vertical component stretches from the x-axis to the most vertical point on the vector. The horizontal component stretches from the start of the vector to its furthest x-coordinate. He also uses a demonstration to show the importance of vectors and vector addition.Ĭomponents of a Vector: The original vector, defined relative to a set of axes. Andersen explains the differences between scalar and vectors quantities. Simplifying vectors in this way can speed calculations and help to keep track of the motion of objects. Whenever you see motion at an angle, you should think of it as moving horizontally and vertically at the same time. You should find you have a right triangle such that the original vector is the hypotenuse.ĭecomposing a vector into horizontal and vertical components is a very useful technique in understanding physics problems. To find the vertical component, draw a line straight up from the end of the horizontal vector until you reach the tip of the original vector. This is the horizontal component of the vector. Next, draw a straight line from the origin along the x-axis until the line is even with the tip of the original vector. To visualize the process of decomposing a vector into its components, begin by drawing the vector from the origin of a set of coordinates. Position, Displacement, Velocity, and Acceleration as Vectors.Unit Vectors and Multiplication by a Scalar. ![]() Using Components to Add and Subtract Vectors.Adding and Subtracting Vectors Using Components. ![]() Adding and Subtracting Vectors Graphically.
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