Method-1:
∣∣
∣∣45−50−1132−3−1∣∣
∣∣=4(11+9)+2(15−55)=80−80=0∴ the three points are collinear.
Method-2:
Distance formula in 3D:
Distance between two points (x1,y1,x1)and(x2,y2,z2)=√(x2−x1)2+(y2−y1)2+(z2−z1)2
Let us call the points as A(4,5,−5), B(0,−11,3) and C(2,−3,−1).
Now, we can calculate the distances →AB, →BC and →AC.
→AB=√42+162+82=√336=4√21
→BC=√22+82+42=√84=2√21
→AC=√22+82+42=√84=2√21
→BC+→AC=→AB.
∴ A,B and C lie on a straight line.
Thus, the points are proved to be collinear.