Cartesian vector notation is a valuable tool in mechanical engineering for representing vectors in three-dimensional space, performing vector operations such as determining the gradient, divergence, and curl, and expressing physical quantities such as the displacement, velocity, acceleration, and force. By using Cartesian vector notation, engineers can more easily analyze and solve problems in various areas of mechanical engineering, including dynamics, kinematics, and fluid mechanics. This notation represents a vector in terms of three components along the x, y, and z axes, respectively.
For example, suppose we have a vector A pointing in the direction (3, −4, 5). In that case, it can be represented using Cartesian vector notation as A = 3i - 4j + 5k, where i, j, and k are unit vectors along the x, y, and z axes, respectively. The unit vectors are defined as i = (1, 0, 0), j = (0, 1, 0), and k = (0, 0, 1).
Cartesian vector notation can be used to perform various vector operations, such as addition, subtraction, and scalar multiplication. For example, if we have two vectors, A = 3i - 4j + 5k and B = 2i + 7j - 3k, we can add them using Cartesian vector notation as follows:
We can also subtract them as follows:
来自章节 2:
Now Playing
Force Vectors
730 Views
Force Vectors
1.2K Views
Force Vectors
1.1K Views
Force Vectors
464 Views
Force Vectors
1.1K Views
Force Vectors
755 Views
Force Vectors
871 Views
Force Vectors
539 Views
Force Vectors
651 Views
Force Vectors
460 Views
Force Vectors
2.0K Views
Force Vectors
622 Views
Force Vectors
779 Views
Force Vectors
468 Views
Force Vectors
289 Views
See More
版权所属 © 2025 MyJoVE 公司版权所有,本公司不涉及任何医疗业务和医疗服务。