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#1 2018-03-11 17:30:20
- Monox D. I-Fly
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[ASK] About Vector and Angle
Given w = |v|∙ u + |u| ∙ v. If θ = ∠(u ∙ w) dan φ = ∠(v ∙ w) then ….
a. Φ – θ = 90°
b. θ + φ= 90°
c. θ = φ
d. θ – φ = 90°
e. θ – φ = 180°
What have I done:
Then I substituted them as |v| and |u| to the given equation and got:
What to do after this? I am stuck.
Actually I never watch Star Wars and not interested in it anyway, but I choose a Yoda card as my avatar in honor of our great friend bobbym who has passed away.
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#2 2018-03-11 19:17:15
- iamaditya
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Re: [ASK] About Vector and Angle
Given w = |v|∙ u + |u| ∙ v. If θ = ∠(u ∙ w) dan φ = ∠(v ∙ w) then ….
What is dan...? Never heard of that function...
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#3 2018-03-11 20:03:06
- Monox D. I-Fly
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Re: [ASK] About Vector and Angle
Ugh, sorry. I meant "and". Forgot to translate that part.
Actually I never watch Star Wars and not interested in it anyway, but I choose a Yoda card as my avatar in honor of our great friend bobbym who has passed away.
May his adventurous soul rest in peace at heaven.
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#4 2018-03-11 21:44:50
- Bob
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Re: [ASK] About Vector and Angle
hi Monox D. I-Fly
I'm not too sure about this, but here's my attempt.
I'll put vectors in bold and magnitudes not bold.
If w = vu + uv then w is a linear combination of u and v
so you can construct the following diagram:
Mark an origin at O. Draw representative vectors from O for u and v. Extend the u line to a point A and the v line to a point B.
Make a parallelogram OACB where OC = w
|OA| = |v|.|u| and |OB| = |u|.|v| so OA = OB.
So OACB is a rhombus.
The diagonals of a rhombus bisect the angles at the vertices so θ = φ
Is this correct?? Not sure.
Bob
Children are not defined by school ...........The Fonz
You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you! …………….Bob 
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#5 2018-03-12 07:23:29
- Alg Num Theory
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Re: [ASK] About Vector and Angle
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Me, or the ugly man, whatever (3,3,6)
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#6 2018-03-12 13:43:22
- Monox D. I-Fly
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Re: [ASK] About Vector and Angle
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How did you get u ∙ w = |u| (u ∙ v) and v ∙ w = |v| (v ∙ u) from w = |v|∙ u + |u| ∙ v?
Actually I never watch Star Wars and not interested in it anyway, but I choose a Yoda card as my avatar in honor of our great friend bobbym who has passed away.
May his adventurous soul rest in peace at heaven.
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#7 2018-03-12 22:49:34
- Alg Num Theory
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Re: [ASK] About Vector and Angle
Sorry, I made a mistake. See my revised post below.
Last edited by Alg Num Theory (2018-03-13 11:32:50)
Me, or the ugly man, whatever (3,3,6)
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#8 2018-03-13 00:19:06
- Bob
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Re: [ASK] About Vector and Angle
We know w = |v|u + |u|v
So u.w = u.(|v|u + |u|v) = |v||u|^2 + |u|u.v
If this is |v| + |u|u.v then |u|^2 = 1. I don't see where it says u is a unit vector.
Am I missing something ?
Bob
Children are not defined by school ...........The Fonz
You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you! …………….Bob
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#9 2018-03-13 11:32:35
- Alg Num Theory
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Re: [ASK] About Vector and Angle
Take two.
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Last edited by Alg Num Theory (2018-03-13 11:33:13)
Me, or the ugly man, whatever (3,3,6)
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#10 2018-03-15 23:36:58
- Libera
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Re: [ASK] About Vector and Angle
Why \pi and not 2\pi?
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#11 2018-03-15 23:47:10
- Alg Num Theory
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Re: [ASK] About Vector and Angle
Why do you want to consider the angle between two vectors to be reflex?
Me, or the ugly man, whatever (3,3,6)
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#12 2018-03-16 02:44:18
- Libera
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Re: [ASK] About Vector and Angle
Why do you want to consider the angle between two vectors to be reflex?
How do you distinguish the case
and are on the same or on the opposite half-planes originated by the line of ?Last edited by Libera (2018-03-16 02:48:22)
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#13 2018-03-16 02:52:19
- Alg Num Theory
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Re: [ASK] About Vector and Angle
Does it matter?
Me, or the ugly man, whatever (3,3,6)
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#14 2018-03-16 03:16:30
- Libera
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Re: [ASK] About Vector and Angle
Does it matter?
It seems to me they are different cases and I don't understand why I should restrict the range of values the angles can assume. Also algebraically the answer would be the same with the wider range. Perhaps with a future thought I'll understand your point of view.
Thanks anyway.
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#15 2018-03-16 03:25:10
- Alg Num Theory
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Re: [ASK] About Vector and Angle
The dot product of two vectors depends (as far as angles are concerned) only on the cosine of the angle in between. Since
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it doesn’t matter whether we take the larger or smaller angle between them. Also, as
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it doesn’t matter whether we measure the angle clockwise or counterclockwise – only the angular magnitude is important. Hence, whether w lies between u and v (i.e. passes through the smaller angle between them) or not is not really important: we can always take theta to be the smaller angle between u and w, and phi the smaller angle between v and w.
Last edited by Alg Num Theory (2018-03-16 03:26:24)
Me, or the ugly man, whatever (3,3,6)
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#16 2018-03-16 04:29:25
- Libera
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Re: [ASK] About Vector and Angle
The dot product of two vectors depends (as far as angles are concerned) only on the cosine of the angle in between. Since
it doesn’t matter whether we measure the angle clockwise or counterclockwise – only the angular magnitude is important.
Thank you for your attempt to be convincing, but it's not matter of calculation.
Let's time make thoughts clear.
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