Concept explainers
A.)
Find the shortest distance between the given point and the line passing through the points
A.)
Answer to Problem 17PS
The distance of given point from the line is 2.12 units.
Explanation of Solution
Given:
The coordinates of points Q is
Hence the direction vector of the line will be
Consider the
Distance between a point Q and line in space with direction vector u is
The coordinates of points Q is
Hence the direction vector of the line will be
Equation of line is given as
Hence the coordinates of a general point on the line will be
Therefore coordinates of point P is
Now cross product of two vectors and is
Therefore
Hence the distance of given point from the line is 2.12 units.
B.)
Find the shortest distance between the given point and the line passing through the points
B.)
Answer to Problem 17PS
The distance of given point from the line is 2.12 units.
Explanation of Solution
Given:
The coordinates of points Q is
Hence the direction vector of the line will be
Consider the vectors in space
Distance between a point Q and line in space with direction vector u is
The coordinates of points Q is
Hence the direction vector of the line will be
Line segment lies on yz-plane as x coordinates remains zero. Thus the equation of line is
Therefore coordinates of point P is
Now cross product of two vectors and is
Therefore
Hence the distance of given point from the line is 2.12 units.
Chapter 11 Solutions
EBK PRECALCULUS W/LIMITS
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