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**Monox D. I-Fly****Member**- From: Indonesia
- Registered: 2015-12-02
- Posts: 1,099

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. May his adventurous soul rest in peace at heaven.

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**iamaditya****Member**- From: Planet Mars
- Registered: 2016-11-15
- Posts: 762

Given w = |v|∙ u + |u| ∙ v. If θ = ∠(u ∙ w) dan φ = ∠(v ∙ w) then ….

What is dan...? Never heard of that function...

Practice makes a man perfect.

There is no substitute to hard work

All of us do not have equal talents but everybody has equal oppurtunities to build their talents.-APJ Abdul Kalam

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**Monox D. I-Fly****Member**- From: Indonesia
- Registered: 2015-12-02
- Posts: 1,099

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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**bob bundy****Administrator**- Registered: 2010-06-20
- Posts: 8,274

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** = v**u** + u**v** 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

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**Alg Num Theory****Member**- Registered: 2017-11-24
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**Monox D. I-Fly****Member**- From: Indonesia
- Registered: 2015-12-02
- Posts: 1,099

Alg Num Theory wrote:

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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**Alg Num Theory****Member**- Registered: 2017-11-24
- Posts: 89
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Sorry, I made a mistake. See my revised post below.

*Last edited by Alg Num Theory (2018-03-13 11:32:50)*

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**bob bundy****Administrator**- Registered: 2010-06-20
- Posts: 8,274

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

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**Alg Num Theory****Member**- Registered: 2017-11-24
- Posts: 89
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Take two.

*Last edited by Alg Num Theory (2018-03-13 11:33:13)*

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**Libera****Member**- Registered: 2018-03-07
- Posts: 16

Alg Num Theory wrote:

Why \pi and not 2\pi?

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**Alg Num Theory****Member**- Registered: 2017-11-24
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Why do you want to consider the angle between two vectors to be reflex?

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**Libera****Member**- Registered: 2018-03-07
- Posts: 16

Alg Num Theory wrote:

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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**Alg Num Theory****Member**- Registered: 2017-11-24
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Does it matter?

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**Libera****Member**- Registered: 2018-03-07
- Posts: 16

Alg Num Theory wrote:

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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**Alg Num Theory****Member**- Registered: 2017-11-24
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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 take the larger or smaller angle between them. Also, as

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)*

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**Libera****Member**- Registered: 2018-03-07
- Posts: 16

Alg Num Theory wrote:

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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