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 →v−→u

Question

3 years ago

7

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 →v−→u

and whose head is at the point halfway from the tip of →u to the tip of →v. Assume all vectors are in standard position.
u: (-1,-1,-1) v:(2,3,-5)

Mathematics

1 answer:

S_A_V [24] · Answer 1 · 2022-07-06T18:56:37+03:00

Û = (-1, -1, -1)
^v = (2, 3, -5)
^v - û = (2 + 1, 3 + 1, -5 + 1) = (3, 4, -4)
Half way from ^v to ^(v - u) = ((3 - 2)/2, (4 - 3)/2, (-4 + 5)/2) = (1/2, 1/2, 1/2)
Halfway from û to ^v = ((2 + 1)/2, (3 + 1)/2, (-5 + 1)/2) = (3/2, 2, -2)

The required vector ^w = ((3/2 - 1/2), (2 - 1/2), (-2 - 1/2)) = (1, 1/2, -5/2)