Question

Find two vectors where the sum of their angles is equal to the angle of their vector sum

Answer 1

@zepdrix @iambatman

Answer 2

Is it a trick question?? xD

Answer 3

I have been stuck on this question for an insane amount of time

Answer 4

Oh and the question specifies that they are nonzero vectors

Answer 5

v = ai + bj
u = ci + dj
u+v = (a+c)i + (b+d)j
angle of v w/ respect to x-axis: v.i = |v||i|cos(o1)
a = sqrt(a^2 + b^2) * cos(o1)
o1 = acos(a/sqrt(a^2 + b^2))

angle of u w/ respect to x-axix: u.i = |u||i|cos(o2)
c = sqrt(c^2 + d^2) * cos(o2)
o2 = acos(c/sqrt(c^2 + d^2))

angle of u+v w/ respect to x-axis:
(u+v).i = |u+v||i|cos(o3)
a+c = sqrt((a+c)^2 + (b+d)^2) * cos(o3)
o3 = acos((a+c)/sqrt((a+c)^2 + (b+d)^2))

o1 + o2 = o3

acos(a/sqrt(a^2 + b^2)) + acos(c/sqrt(c^2 + d^2)) = acos((a+c)/sqrt((a+c)^2 + (b+d)^2))

The expression above must be satisfied in order to find two vectors that attend the requirements.

Note that if u and v are linear combinations of each other, the resultant sum will have the same angle.
Example: u = 1i + 2j and v = 5i + 10j
u + v = 6i + 12j

Answer 6

Holy cow

Answer 7

Umm ok

Answer 8

I have never seen anything remotely like that in my entire life

Answer 9

hahahah maybe there is a simpler way to solve this but for now that is the only method i found

Answer 10

Ok, well thanks anyways. If you know ANYBODY that could help, I would very much appreciate it!

Answer 11

@ganeshie8

Answer 12

@jim_thompson5910

Answer 13

the only time I think that happens is when you have one vector reflected over the x axis

Answer 14

say we initially have this vector

Answer 15

I have been stuck on this question for so long

Answer 16

and say the angle from the x axis to the vector is 30 degrees

Answer 17

ok

Answer 18

if you reflect it over the x axis, you get

Answer 19

Use magnitude too. I think thats what they want in the question

Answer 20

the angles add to 30 + (-30) = 0 degrees

Answer 21

*Please use magnitude as well :)

Answer 22

The issue is that they want me to use vector addition

Answer 23

They want the angle of a+the angle of b to equal the angle of r

Answer 24

the resultant vector is this

Answer 25

so we can see that vector z has an angle of 0 degrees

Answer 26

Oh, that makes sense!! Thanks so much!!!

Answer 27

np