Answer:
[tex]u_{v}=-\frac{24}{\sqrt{745} }i +\frac{13}{\sqrt{745} } j[/tex]
Step-by-step explanation:
The initial point of the vector is at (7,-9).
The terminal point of the vector is at (-17,4).
First, we need to find the same vector with initial point at the origin of the coordinate system. We do that by finding its horizontal length and its vertical length.
[tex]\Delta x = -17 - 7=-24\\\Delta y = 4-(-9)=13[/tex]
So, the vector with initial point at the origin is
[tex]v=-24i+13j[/tex]
Where [tex]i[/tex] represents horizontal direction and [tex]j[/tex] represents vertical direction.
Now, we need to find the module of this vector
[tex]|v|=\sqrt{(-24)^{2}+(13)^{2} }=\sqrt{576+169}\\ |v|=\sqrt{745}[/tex]
The uni vector is defined by the quotient between the vector and its module.
[tex]u_{v} =\frac{v}{|v|}[/tex]
Replacing each part, we have
[tex]u_{v}=\frac{-24i+13j}{\sqrt{745} }\\ u_{v}=-\frac{24}{\sqrt{745} }i +\frac{13}{\sqrt{745} } j[/tex]
Therefore, the right answer is the third choice.
