What Does a Unit Vector Field Look Like in Cartesian Coordinates?

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SUMMARY

The discussion focuses on understanding unit vector fields in Cartesian coordinates, specifically how to represent a vector S with a magnitude of 1. The user successfully solved parts (a) and (b) using the point P(2,4,3) and the formula a(S) = S/|S|. The challenge arises in part (c), where the user seeks clarification on the mathematical representation of the locus of points where the magnitude of S equals 1. The key takeaway is that the locus can be expressed mathematically in terms of x, y, and z coordinates.

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Hello guys !

i have this problems while solving problems on vector calculus ..

Fps0q98.png



i solved (a) , (b)
as i put P(2,4,3) in the formula of S and i solved it and i solved (b) as a(S)= S/lSl

but in (c) i don't how what should i do to solve it ..please help me guys ..Thank you
 
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As you have solved b you must have already computed |S|. From having that expression you should be able to progress.
 
Where the magnitude of S is 1, what does that look like mathematically in terms of x y and z? In other words, you have a locus of points, and all of these points, when you calculate the magnitude of S there, it's equal to 1. What does this look like mathematically?
 

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