Unit Vector z in Spherical Terms: (1, 0, 0)

[formulajoe]

at (2,3,-4) express the unit vector z in spherical terms.
express the unit vector r in rectangular terms.

for the first part, would it just be (1,X,0)
fi should be zero because that's the angle the line makes with the z axis, and since this is going to be parallel to the z-axis this should be zero and theta shouldn't matter. and the unit vector r should just be the point made into a vector right? since the unit vector r is pointing away from the origin. so at (2,3,-4) its going to be in the direction of (2,3,-4).
should it have a different magnitude?

 

[MathStudent]

I assume (2,3,-4) describes a position vector

By definition a unit vector is a vector with a magnitude of 1.
so in the rectangular system, you result should be a vector with the same direction of (2,3,-4) but with a magnitude of 1.

for your answer in spherical coordinates it seems wrong, but maybe I am misunderstanding the question... It seems that you are asking to convert the position vector (2,3,-4) into a unit vector and give the answer in spherical coordinates. Is that right? if so then your answer is incorrect as it is not parallel to the z axis since it has both nonzero x and y components and thus would make an angle wrt both the z axis and the x axis.

 

[formulajoe]

(2,3,-4) is a point. it wants me to represent the z unit vector in the spherical system. basically i think it wants me to represent the z unit vector from that point using spherical coordinates.

 

[MathStudent]

I really doubt that is what they are asking you, because that is basically pointless, If it is, than I don't know what to tell you,,, I'm not saying its impossible, but I wouldn't know. It seems much more likely that they want you to describe the unit vector having the same direction as the position vector (2,3,-4) but in spherical coordinates.

 

[formulajoe]

heres exactly what it says
at point T(2,3,-4) express a sub z in the spherical system and a sub r in the rectangular system.