Find the distance of the point (1,+ and-6,-1) from the line with vector equation r=i+7j+-1k+t(3i+12j-4k)

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- Jul 14th 2006, 08:32 PMkingkaisai2Vector-finding distance, difficult/confusing
Find the distance of the point (1,+ and-6,-1) from the line with vector equation r=i+7j+-1k+t(3i+12j-4k)

- Jul 15th 2006, 06:13 AMCaptainBlackQuote:

Originally Posted by**kingkaisai2**

(1,-6,-1).

2) By the distance from the point p to the line r(t) I take it that you mean

the minimum distance.

One way (not necessarily the simplest) to do this is to write:

$\displaystyle s(t)^2=|p-r(t)|^2$,

then differentiate this with respect to t and set the derivative to zero and

and solve the resulting equation for t, which will give the t corresponding to

the closest point on the line to the given point, which can then be used to

find the actual minimum distance.

RonL