Notice, too, that the direction of the x-component is − i ^ − i ^, which is antiparallel to the direction of the + x-axis hence, the x-component vector D → x D → x points to the left, as shown in Figure 2.17. The vector x-component D → x = −4.0 i ^ = 4.0 ( − i ^ ) D → x = −4.0 i ^ = 4.0 ( − i ^ ) of the displacement vector has the magnitude | D → x | = | − 4.0 | | i ^ | = 4.0 | D → x | = | − 4.0 | | i ^ | = 4.0 because the magnitude of the unit vector is | i ^ | = 1 | i ^ | = 1. Often, the latter way is more convenient because it is simpler. Notice that the physical unit-here, 1 cm-can be placed either with each component immediately before the unit vector or globally for both components, as in Equation 2.14. The vector points from the origin point at b to the end point at e.
![missing component multisim 14.1 missing component multisim 14.1](https://content.instructables.com/FF8/NT87/J1MF0UDJ/FF8NT87J1MF0UDJ.png)
The scalar x- and y-components of the displacement vector areįigure 2.17 The graph of the displacement vector. We identify x b = 6.0 x b = 6.0, x e = 2.0 x e = 2.0, y b = 1.6 y b = 1.6, and y e = 4.5 y e = 4.5, where the physical unit is 1 cm. Finally, substitute the coordinates into Equation 2.12 to write the displacement vector in the vector component form. Substitute the coordinates of these points into Equation 2.13 to find the scalar components D x D x and D y D y of the displacement vector D → D →. The origin of the displacement vector is located at point b(6.0, 1.6) and the end of the displacement vector is located at point e(2.0, 4.5). J ^ j ^ on the y-axis points vertically upward. Therefore, the unit vector i ^ i ^ on the x-axis points horizontally to the right and the unit vector
![missing component multisim 14.1 missing component multisim 14.1](https://content.instructables.com/ORIG/FP8/WYDJ/J1QP1C1I/FP8WYDJJ1QP1C1I.png)
The origin of the xy-coordinate system is the lower left-side corner of the computer monitor. If you move the pointer to an icon located at point (2.0 cm, 4.5 cm), what is the displacement vector of the pointer? In this way, following the parallelogram rule for vector addition, each vector on a Cartesian plane can be expressed as the vector sum of its vector components:Ī mouse pointer on the display monitor of a computer at its initial position is at point (6.0 cm, 1.6 cm) with respect to the lower left-side corner. In the Cartesian system, the x and y vector components of a vector are the orthogonal projections of this vector onto the x- and y-axes, respectively. The vector y-component is a vector denoted by A → y A → y. The vector x-component is a vector denoted by A → x A → x. The x-coordinate of vector A → A → is called its x-component and the y-coordinate of vector A → A → is called its y-component. In a similar fashion, a vector A → A → in a plane is described by a pair of its vector coordinates. In a rectangular (Cartesian) xy-coordinate system in a plane, a point in a plane is described by a pair of coordinates ( x, y). For example, if you ask someone for directions to a particular location, you will more likely be told to go 40 km east and 30 km north than 50 km in the direction 37 ° 37 ° north of east. Even in everyday life we naturally invoke the concept of orthogonal projections in a rectangular coordinate system. Vectors are usually described in terms of their components in a coordinate system.
![missing component multisim 14.1 missing component multisim 14.1](https://pcbwayfile.s3-us-west-2.amazonaws.com/project/21/04/01/0522119923344.png)
By the end of this section, you will be able to: