Component Vectors: Finding Along Non-Perpendicular Lines/Axes

Thread starter Ali Asadullah
Start date Mar 14, 2010
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Component Vectors

In summary, a component vector is a vector used to represent a specific part of a larger vector in physics and engineering. To find a component vector along a non-perpendicular line or axis, you would need to calculate the angle and use trigonometric functions. Component vectors can have negative values, indicating direction. To add or subtract component vectors, you would combine the corresponding components. Real-world applications include navigation systems, physics and engineering analysis, and computer graphics.

Mar 14, 2010

Ali Asadullah

How can we find component vectors along non-perpendicular lines/axis? Please illustrate with example.

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Mar 14, 2010

CompuChip

Science Advisor

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In the same way as you would with perpendicular axes.
The inner product just projects one vector onto some axis (i.e. another vector), it doesn't depend on separate axes to be perpendicular.

1. What is a component vector?

A component vector is a vector that represents the magnitude and direction of a specific component, or part, of a larger vector. It is often used in physics and engineering to break down complex forces or motions into simpler, easier to understand components.

2. How do you find a component vector along a non-perpendicular line or axis?

To find a component vector along a non-perpendicular line or axis, you would first need to determine the angle between the vector and the line or axis. Then, you can use trigonometric functions, such as sine, cosine, and tangent, to calculate the magnitude and direction of the component vector.

3. Can component vectors have negative values?

Yes, component vectors can have negative values. This indicates the direction of the vector, with a negative value representing a vector in the opposite direction of a positive value.

4. How do you add or subtract component vectors?

To add or subtract component vectors, you would first need to determine the component vectors for each individual vector. Then, you can add or subtract the corresponding components to get the final component vector.

5. What are some real-world applications of component vectors?

Component vectors have many real-world applications, such as in navigation systems, where they are used to calculate the direction and magnitude of movement. They are also commonly used in physics and engineering to analyze forces and motions, and in computer graphics to create 3D models and animations.