If these points are collinear then area of triangle formed by it is 0.
1/2[-1(p+1)+2(-1-3)+5(3-p)]=0
=[-p-1+2(-4)+5(3-p)]=0
=-p-1-8+15-5p=0
=6-6p=0
=6=6p
P=1. Ans

Introduction:
In this problem, we are given three points (-1,3), (2,p), and (5,-1) and we need to find the value of p for which the points are collinear.

Method:
To solve this problem, we will use the concept of collinearity of points.

Collinearity of points:
Three points A, B, and C are said to be collinear if they lie on the same straight line.

Using the slope formula:
We will use the slope formula to check if the three points are collinear. The slope of a line passing through two points (x1, y1) and (x2, y2) is given by the formula:

m = (y2 - y1)/(x2 - x1)

Calculations:
We will first find the slope of the line passing through the points (-1,3) and (2,p).

m1 = (p - 3)/(2 - (-1)) = (p - 3)/3

Similarly, we will find the slope of the line passing through the points (2,p) and (5,-1).

m2 = (-1 - p)/(5 - 2) = (-1 - p)/3

Since the three points are collinear, the slope of the line passing through the points (-1,3), (2,p), and (5,-1) must be the same.

m1 = m2

(p - 3)/3 = (-1 - p)/3

p - 3 = -1 - p

2p = 2

p = 1

Conclusion:
Therefore, the value of p for which the points (-1,3), (2,p), and (5,-1) are collinear is p = 1.