Distance between a point and a Vector.?

There is a vector from point A to B


VectorAB= %26lt; 4,1,-2%26gt;


Then there is a point C(4,1,2) .





What is the shortest distance between C, and vector AB?

Distance between a point and a Vector.?
You must know the coordinates of either A or B to answer this fully. As it is states, C could be in Vector AB. Thus, the shortest distance is zero.


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OK. So point A is at (0,0,2) B is at (4,1,0) and point C is at C(4,1,2). Consider A, B, and C veritces of a triangle. Find the lengths of each side. Then, ignore the 3D stuff. Find the altitude of triangle ABC from C to side AB.





For lengths of sides, use


(x2-x1)^2 + (y2-y1)^2 + (z2-z1)^2 = d^2.





This works for this specific problem when distance is the main concern.





The previous poster has the hardcore, pure math method that works in more general cases.
Reply:Find the vector orthogonal to AB that passes through the point C. Then calculate the length of that vector.

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