Re: Question in Geometry

On Sep 24, 7:44 am, Virgil <Vir...@xxxxxxxxx> wrote:
In article
<018e4989-1f34-44ea-9d7d-e2a167f12...@xxxxxxxxxxxxxxxxxxxxxxxxxxx>,





 miki <miki.li...@xxxxxxxxx> wrote:
On Sep 23, 9:33 pm, Virgil <Vir...@xxxxxxxxx> wrote:
In article
<ea92ae29-6a7b-4499-b23f-f6effcd52...@xxxxxxxxxxxxxxxxxxxxxxxxxxx>,

 miki <miki.li...@xxxxxxxxx> wrote:
Hello all,

I have a question in Geometry, It would be great to have some help.

Let V_1 be a 3-dim vector in a cartesian plane (XYZ). For simplicity,
let V_1 be of the kind
(a, 0, 0) where a is unknown. Now, consider another vector V_2 given
in spherical coordinates
(phi, theta, R) where phi, theta and R are known. Both vectors are in
the same 3-dim space with common origin.
Find the angle between V_1 and V_2

Thanks,
Miki

Assuming both vectors have strictly positive lengths, convert the
vector, V2, in spherical coordinates to rectangular coordinates like
those of V1, then , where V1.V2 represents the dot product of V1 and V2,  
and |V| = sqrt(V.V) represents the length of V, the angle is given by

angle = arccos( (V1/|V1|).(V2/|V2|) )

Thanks, but the problem is that V1 is unknown.
Is there any closed formula for the angle between V1 and V2 as a
function of only the angles phi and theta?

Miki

If only  the length of V! is unknown, but the spherical angles are
known, make V1 a unit vector, so |V1| = 1.

Note that the angle between two vectors is independent of their lengths,
provided, of course, that neither of those two lengths is zero.- Hide quoted text -

- Show quoted text -

No. I dont know anything about V1, but the fact that it is of the form
[a, 0, 0] where a > 0.
I dont know "a" so I cant normalize it. I also think that the angles
between V1 and V2 is independent of their length, but I dont know how
to calculate the angle given only phi and theta and V2.
Thanks

Thats the question.
.

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