Question

Can three vectors in the xy plane have u · v < 0 and v · w < 0 and u · w < 0?

Answer 1

I don't think so

Answer 2

It depends on your plane and what the vectors are measuring

Answer 3

Dot product less than zero means obtuse angle

Answer 4

all three angle can't be obtuse on one plane

Answer 5

angle between u and v
angle between u and w
angle between w and v

Answer 6

all are obtuse

Answer 7

soooorrrryy i forgot we were talking about vectors hehe

Answer 8

So since they would all be obtuse, it wouldn't be possible?

Answer 9

However, for instance,

Take:
u = (1, 0),
v = (−1/2, (square root of 3)/2),
w = (−1/2, − (square root of 3)/2).

Then u • v = v • w = u • w = −1/2

Which would, in fact, make it possible....right?

Answer 10

Yes

Answer 11

Okay, I thought so.

Answer 12

When figuring out this problem the key is to ask if three obtuse angle are possible on a plane. So if we arbitrarily choose two obtuse angel say 100 degree and 120 degree. Subtract the sum of the angel from 360 and we get an obtuse third angle.