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

`u_(v)=-(24)/(√(745) )i +(13)/(√(745) ) j`

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) }=√(576+169)\\ |v|=√(745)`

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

`u_(v) =(v)/(|v|)`

Replacing each part, we have

`u_(v)=(-24i+13j)/(√(745) )\\ u_(v)=-(24)/(√(745) )i +(13)/(√(745) ) j`

Therefore, the right answer is the third choice.

Answer 2

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)