Unit vector and direction cosines?
Moderator: msmod
Unit vector and direction cosines?
I understand that we find the direction cosines (see the drawing) by dividing the vector components (i, j and k) by the vector magnitude. Ok. I can understand cosine formed by the vector magnitude and kaxis but I don't understand cosine formed by i and j  components of the vector. If I understand right cos(alpha) is formed by icomponent divided by the vector PROJECTION (not the vector magnitude) on the plane devoted by iaxis and jaxis, therefore cos(beta) is formed by jcomponent divided by the vector projection (not the vector magnitude). So why is the vector magnitude used to define cos(alpha) and cos(beta)?
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Re: Unit vector and direction cosines?
Gday Boris,
you have a diagram a bit like the one in
http://www.animations.physics.unsw.edu. ... ors.htm#3d
You might want to consider the vector that I've called h – the projection onto the x,y plane.
Take the components here, and then consider the z components
Best
Joe
you have a diagram a bit like the one in
http://www.animations.physics.unsw.edu. ... ors.htm#3d
You might want to consider the vector that I've called h – the projection onto the x,y plane.
Take the components here, and then consider the z components
Best
Joe
Re: Unit vector and direction cosines?
Thanks a lot, Joe.
My problem was that I didn't know that there is not only "scalar projection" but and "vector projection". They are different: "scalar projection" is just a number and "vector projection" is a vector.
Have a nice weekend
My problem was that I didn't know that there is not only "scalar projection" but and "vector projection". They are different: "scalar projection" is just a number and "vector projection" is a vector.
Have a nice weekend