Question

If u and v are the vectors below, find the vector w whose tail is at the point halfway from the tip of v to the tip of u and whose head is at the point halfway from the tip of u to the tip of u-v.

u = (-2,-4,-5)
v = (-3, 5, -1)

answer: (2, -7, -3/2)

Answer 1

Find two vectors pointing to those midpoints.
Then subtract the vectors from each other.

Answer 2

so, (1/2(U+V))-(1/2(U-V))?

Answer 3

Not sure how you got that.

Answer 4

ok, so one half of the way from u to v i translated into 1/2U+1/2V. The second half from u-v, based on one half of the way along U. That is 1/2U-1/2V. THen I subtracted the two from each other. Does that make sense?

Answer 5

So we know \(\mathbf{w}\) is the difference between head and tail.\[
\mathbf{w}=\mathbf{w}_h-\mathbf{w}_t
\]Then we know:

"whose tail is at the point halfway from the tip of v to the tip of u" \[
\mathbf{w}_t=\frac{1}{2}(\mathbf{u}+\mathbf{v})
\]
"whose head is at the point halfway from the tip of u to the tip of u-v"\[
\mathbf{w}_h=\frac{1}{2}(\mathbf{u}+(\mathbf{u}-\mathbf{v}))
\]
Does this model make sense?

Answer 6

Ohhhhh. I see. I forgot to do 1/2U. And thats important because half way up U

Answer 7

Wait I think my midpoint formula is wrong.

Answer 8

whast wrong with it?

Answer 9

whats*

Answer 10

Wait never mind it is correct, false alarm.

Answer 11

Ok good. I will try it and let you know

Answer 12

it doesnt seem to work

Answer 13

ya ive attempted the question three times now, and none of the answers I get are correct