Question: how do I introduce vector and differentiate it?

Hello

I was trying to introduce vector r_vec that has 3 components in x,y,z

I've attached my file, I've 2 questions here

first, why isn't the vector shown in as r_vec = () ei + () ej + () ek instead appears as a column vector

second, why doesn't it accept differentating

thank you
 

restart````

r := sqrt(VectorCalculus:-`+`(x^2, VectorCalculus:-`+`(y, VectorCalculus:-`-`(VectorCalculus:-`*`(z, 1/VectorCalculus:-`*`(tan, alpha))))^2))

(x^2+(y-z/(tan*alpha))^2)^(1/2)

(1)

 

theta := arctan((y-z)/x)

arctan((y-z)/x)

(2)

Z := VectorCalculus:-`*`(z, 1/VectorCalculus:-`*`(sin, alpha))

z/(sin*alpha)

(3)

with(VectorCalculus): 

r_vec := `<,>`(VectorCalculus:-`*`(r, `cos&theta;`), VectorCalculus:-`+`(VectorCalculus:-`*`(VectorCalculus:-`*`(r, sin), theta), VectorCalculus:-`*`(VectorCalculus:-`*`(Z, cos), alpha)), VectorCalculus:-`*`(VectorCalculus:-`*`(Z, sin), alpha))

Matrix(3, 1, {(1, 1) = sqrt(x^2+(y-z/(tan*alpha))^2)*`cos&theta;`, (2, 1) = sqrt(x^2+(y-z/(tan*alpha))^2)*sin*arctan((y-z)/x)+z*cos/sin, (3, 1) = z})

(4)

diff(r_vec, r)

Error, (in VectorCalculus:-diff) invalid input: diff received (x^2+(y-z/(tan*alpha))^2)^(1/2), which is not valid for its 2nd argument

 

``


 

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