Does anyone know how to resolve forces in 3 directions?

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To resolve forces in three dimensions, one must use the dot product of the vector with the corresponding unit vector for each direction. The displacement vector given is i + 2j - k, and understanding the geometric interpretation of the dot product can aid in this process. It's important to consider the components of the vector along each axis to accurately resolve it. Additional resources on tensors may provide further insights into this topic. A clear understanding of these concepts will facilitate the resolution of forces in three dimensions.
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Homework Statement
3 dimensional vectors
Relevant Equations
I have been given a question as follows :
A force 𝐹=2𝑖 +3𝑗 +𝑘 N moves a particle from 𝑟1=𝑖+2𝑗 m to 𝑟2=2𝑖 +4𝑗−𝑘 m.
Find the component of 𝐹 in the direction of the displacement. Give your answer to 3.s.f
I know the direction of the displacement is: i+2j-k, but I do not know how to resolve in 3 dimensions. If anyone knows how to do this could they please help me. Thank you.
 
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Please look up 'tensor' and maybe show a little more work.
 
sysprog said:
Please look up 'tensor' and maybe show a little more work.
thanks
 
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The component of a vector in a particular direction is the dot product of the vector with the unit vector in that direction. You should be able to rationalise this with a geometrical argument (how is the dot product defined?).
 
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