Chapters
In this article, we have jotted down various distance formulas. These formulas will help you to solve distance related problems easily. So, let us get started.
Distance Between Two Points in a Plane
Distance between two points A and B tells us the shortest distance between these two points. Two points A and B along with their coordinates are shown in the figure below:
and the coordinates of point B are 
, The formula to compute the distance between these two points is given below:
Consider the following example:
Calculate the distance between point A (5, -2) and point B (8, 3).
Use the following formula to calculate the distance between these two points:
Distance from a Point to a Line in a Plane
Distance from a point to a line is the shortest distance between a line and point P. In the following figure, you can see a line r and point P. The shortest distance between point P and line r is depicted by a perpendicular line 
.
Distance to the Origin in Plane
Consider the following example:
Calculate the distance between the line r whose equation is 2x + 5y + 2 = 0 and origin O.
Use the following formula to compute the distance between the line r and origin O.
Distance between Parallel Lines in a Plane
The distance between two parallel lines in a plane shows the shortest distance between two lines in a plane. The following figure shows two parallel lines r and s in a plane.
and the equation of the line 2 is 
. The shortest distance between these lines can be calculated using the following formula:
Consider the following example:
Calculate the distance between two parallel line r which has an equation 3x + 5y + 1 = 0 and line s which has an equation 3x + 5y + 7 = 0.
Use the following formula to compute the distance:
Substitute the values in the formula like this:
Distance Between Two Points in a Space
The minimum distance between two points in a three dimensional space is calculated using the following formula:
Consider the following example:
Calculate the distance between two point A (3, 4, 5) and B (7, 1, 4).
Use the following formula to calculate the distance:
Substitute the values in the above formula:
Point-Line Distance - Space
The distance from a point, P, to a line, r, tells us the minimum distance from the point to one of many points on the line.
The formula to compute the distance between a line r and the point P is given below:
Here, 
reflects the direction vectors and 
reflects the distance between the point P and point A on the line.
Consider the following example:
.First, we have to calculate 
.We need to treat each of the 
, 
, and 
coefficients on the vector i, j, and k. 
= 
Now, we will make 2 groups. One group will contain all the values that have t and the other group will consist of all the values that do not have t like this:
= (i + 3j + 4k) + (2ti + 1tj + 1tk)
Now, we will factor out t from the second group like this:
= 
The coefficients in the first group show the point from which the line passes through and the coefficients in the second group reflect the direction vectors.
Hence, the direction numbers for the line are 
and the coordinates of the point through which the lines passes are 
.
We have to calculate the distance between the point P (1 , 2, 5) and point on the line A (1, 3, 4).
Since have both A and P, hence we can easily calculate 
like this:
Now, we will find the cross product of 
as shown below:
Put these values in the following formula to get the distance:
Find various Maths tuition on Superprof.
Distance between a Point and a Plane in a Space
is given below: 
Consider the following example:
Calculate the distance between a point P (3, 6, 7) and the plane 
Use the following formula to calculate the distance:
Substitute the values in the above formula:
Did you like this article? Rate it!
Loading...
I WANT TO CONTINUE WITH SOLVED PROBLEMS OF APPLICATION OF CROSS PRODUCTS OF VECTORS