help me

[wise agate]

I have a question. Who can help me solve it?

[topaz helm]

You can work with |a+b|² and you know |a| = 1 = |b|

[wise agate]

Of course

[wise agate]

What is the final result?🤔

[topaz helm]

Last hint: || |a+b|² = |a|² + |b|² + 2<a,b> ||

[wise agate]

2<a,b> What do you mean by ?🤔

[topaz helm]

dotproduct

[wise agate]

This question should be used dotproduct?

I think it can be like this.

[topaz helm]

Taking a look at |a+b|²

,, \abs{\vec{a}+\vec{b}}^2 = \abs{\vec{a}}^2 + \abs{\vec{b}}^2 + 2\vec{a}\vec{b} = 1 \iff 2 + 2\vec{a}\vec{b} = 1 \iff 2\vec{a}\vec{b} = -1

[analog laurel]

𝔸dωn𝓲²s

[topaz helm]

yes

[wise agate]

So am I right to write like this?🤔

[topaz helm]

yes

now take the square root

[analog laurel]

𝔸dωn𝓲²s

𝔸dωn𝓲²s

[topaz helm]

Property of dot product basically

[wise agate]

Root No. 3？

[topaz helm]

ye

[wise agate]

Thanks for the guidance.

❤️