lf u and vare the vectors below find the vector w whose tail

lf u and vare the vectors below, find the vector w whose tail is at the point halfway from the tip of v to the tip of and whose head is at the point halfway from the tip of u to the tip of it-v. Assume all u vectors are in standard position.

Solution

u = <-2 , -4 , -3>
v = <-2 , 4 , 2>

First we find the point halfway from the tip of v to the tip of u :
This would be the midpoint between u and v

So, using midpoint formula :
The point is : (-2 + (-2))/2 , (-4 + 4)/2 , (-3 + 2)/2

---> (-2 , 0 , -1/2)

So, the tail of w = <-2 , 0 , -1/2>

u - v = <-2 , -4 , -3> - <-2 , 4 , 2>
u - v = <0 , -8 , -5>

Halfway between the tip of u to the top of u - v is :

(<-2 , -4 , -3> + <0 , -8 , -5>) / 2

---> <-2 , -12 , -8> / 2

---> <-1 , -6 , -4>

So, head of w = <-1 , -6 , -4>
And tail of w = <-2 , 0 , -1/2>

Therefore, w itself is :
Head - tail

<-1 , -6 , -4> - <-2 , 0 , -1/2>

<-1 + 2 , -6 - 0 , -4 + 1/2>

<1 , -6 , -7/2>

So, vector w is : <1 , -6 , -7/2> -----> ANSWER