Answer:
The direction of [tex]\overrightarrow{P_1P_2}[/tex] is (4,4,-5).
The midpoint of the line segment [tex]\overline{P_1P_2}[/tex] is in (-1 , 3 , 2.5)
Step-by-step explanation:
The direction of a vector that goes from the initial point A to the final point B can be calculated as the subtraction of B with A. In this case:
[tex]\overrightarrow{P_1P_2}=\vec{P_2}-\vec{P_1}=(1, 5, 0) - (-3, 1, 5)=(4, 4, -5)[/tex]
The midpoint of the line segment between two points A and B can be obtained as the halving of the addition of the vector A with the vector B. The line segment AB and the vector A+B make a rhombus. These lines will cross each other in their respective mediatrix. Therefore, if you obtain the point of the mediatrix of the vector A+B, you will find the midpoint of the segment AB. In this case:
[tex]P_{mid1-2}=(\vec{P_1}+\vec{P_2})/2=\frac{1}{2}[(-3, 1, 5)+(1, 5, 0)]=(-1, 3, 2.5)[/tex]
