(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

a) Find the shortest distance between the surface A: (x+2)^2+(y-3)^2+(z-5)^2=9 and the line that passes by the points P0:(9,8,10) and P1:(16,6,14).

b)Find the coordinates of a point on the line and a point on the surface that are nearest to each other.

2. Relevant equations

Surface is a sphere, centered around PC:(-2, 3, 5).

Distance Line-Point = [tex] \frac {||P0P1 x P0PC||}{||POP1||}[/tex]

3. The attempt at a solution

I found the distance between the line and the center of the sphere, then substracted by the radius (3) of the sphere, to find a distance of approx. 7.355 units.

However, how can I now find the Vector that defines the line of the shortest distance between the sphere and the line? Once I have the equation of that line, I can solve for b) by finding the intersects.

I know I'm looking for a perpendicular line to the one that is defined by POP1, so that the scalar product must equal 0, however in 3D, there is an infinite answer of perpendicular lines.

Thanks.

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# Homework Help: Vectors: Distance between 3D object and line

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