Question

Vector v has its initial point at (7, -9) and its terminal point at (-17, 4). Which unit vector is in the same direction as v?

Answer 1

The answer is the option C 

Find unit vector.

Definition of unit vector :

u is a unit vector, it has the same direction as v then 

v--------------(7,-9)         (-17,4)

v=(-24,13)

u is a unit vector, it has the same direction as v

magnitude of v---------(-24^2+13^2)^0.5=725^0.5

 u=(-24/(725)^.5),(13/(725)^.5)

Answer 2

Answer:

$u_{v}=-\frac{24}{\sqrt{745} }i +\frac{13}{\sqrt{745} } j$

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.

$\Delta x = -17 - 7=-24\\\Delta y = 4-(-9)=13$

So, the vector with initial point at the origin is

$v=-24i+13j$

Where $i$ represents horizontal direction and $j$ represents vertical direction.

Now, we need to find the module of this vector

$|v|=\sqrt{(-24)^{2}+(13)^{2} }=\sqrt{576+169}\\ |v|=\sqrt{745}$

The uni vector is defined by the quotient between the vector and its module.

$u_{v} =\frac{v}{|v|}$

Replacing each part, we have

$u_{v}=\frac{-24i+13j}{\sqrt{745} }\\ u_{v}=-\frac{24}{\sqrt{745} }i +\frac{13}{\sqrt{745} } j$

Therefore, the right answer is the third choice.