The distance of the point(3,0,5)from the line parallel to the vector (6i+j-2k) and passing through the point(8,3,1) is..?
2 Answers
We write the general distance between a point on the line and the given point, then complete the square to minimize it, giving a distance of
Explanation:
There are a few different ways to do this one. Let's write the squared distance from our point to a general point on the line, and find which of those points minimizes the distance.
Our line has direction vector
The distance
We minimize
Clearly this is minimized at t=-1 at which point
Explanation:
The scalar equation of the family of planes normal the vector
Find the value of C for the plane that contains the point
The equation of the plane normal to the line that contains the point
The vector equation of the line is:
The parametric equations for the line are:
To find the value of t where the line intersects the plane substitute the parametric equations into the scalar equation for the plane:
Use the vector equation of the line to find the point on the plane at
Use the distance formula to find the distance from