Collinearity Of Points

To solve the problem, we need to find the distance between the two given points: and .

1. Understanding the Distance Formula:
The distance between two points and is given by:

2. Substituting the Values:
Here,
So,

3. Simplifying the Expressions:

4. Final Calculation:

Final Answer:
The distance between the points is

To solve the problem, we need to determine the value of for which the three points , , and are collinear.

1. Understanding the Condition for Collinearity:
Three points are collinear if the area of the triangle formed by them is zero. The area of triangle formed by three points is given by:

2. Substituting the Given Points:
Let , , and .

Using the formula:

3. Simplifying the Expression:

4. Solving the Equation:
Since the absolute value is zero:

Final Answer:
The value of is .