# Vector-finding distance, difficult/confusing

• July 14th 2006, 09:32 PM
kingkaisai2
Vector-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)
• July 15th 2006, 07:13 AM
CaptainBlack
Quote:

Originally Posted by kingkaisai2
Find the distance of the point (1,+ and-6,-1) from the line with vector equation r=i+7j+-1k+t(3i+12j-4k)

1) (1,+ and-6,-1) is not a point but if anything it is two points (1, 6,-1) and
(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:

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

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