Component Vectors: Finding Along Non-Perpendicular Lines/Axes

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To find component vectors along non-perpendicular lines or axes, the inner product can be utilized to project one vector onto another without the need for perpendicularity. An example can illustrate this process by demonstrating how to calculate the projection of a vector onto a non-perpendicular axis using the inner product formula. This method allows for the determination of components in any direction, regardless of the angle between the axes. The key takeaway is that the inner product effectively facilitates vector decomposition along any chosen direction. Understanding this concept enhances the ability to analyze vector components in various applications.
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How can we find component vectors along non-perpendicular lines/axis? Please illustrate with example.
 
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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.
 

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