- #1

LMHmedchem

- 20

- 0

If I have point B in an orthogonal n-space and point C at the origin of the same space,

Code:

```
point_B = 0.03299720 0.00585822 -0.36979000 -0.43413200 -0.60787700 0.61335300 0.76003400
point_C = 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
```

this would make the vector and from point_B to point_C,

Code:

```
vBC = -0.03299720 -0.00585822 0.36979000 0.43413200 0.60787700 -0.61335300 -0.76003400
|vBC| = 1.28440897
```

If I were to place a hypersphere around point_B at a radius, say 10% of |vBC| = 0.128, how would I define the equation of that hypersphere and the coordinates of the intersection between the hypersphere and vBC?

My understanding is the the equation for a hypersphere in R6 would be,

$${x}_{1}^{2} + {x}_{2}^{2}+{x}_{3}^{2}+{x}_{4}^{2}+{x}_{5}^{2}+{x}_{6}^{2}={R}^{2}$$

or in this case, the set of all points that satisfy,

$${x}_{1}^{2} + {x}_{2}^{2}+{x}_{3}^{2}+{x}_{4}^{2}+{x}_{5}^{2}+{x}_{6}^{2}=1.28$$

I assume that we would find the equation of the line BC and then the simultaneous solution to both equations.

I am not really sure how to generate the equation of the line BC in R6. I am never quite sure if this is a line, plane, or hyperplane. As far as the intersecting point, will there actually be a point that is both on the line and in the hypersphere, or can we only find the point on BC that is closest to the hypersphere?

Thanks again,

**LMHmedchem**