Does anyone know how to resolve forces in 3 directions?

[FailedPaper5712]

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.

 

[sysprog]

Please look up 'tensor' and maybe show a little more work.

 

[FailedPaper5712]

Please look up 'tensor' and maybe show a little more work.

thanks

 

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?).