/sci/ - Science & Math

[Anonymous No.4248228]

One of the proofs in my LA book has this line:
<span class="math">\left \| \hat{x}+\hat{y} \right \|^2=\left \| \hat{x} \right \|^2+2x\cdot y+\left \| y \right \|^2=2(x\cdot y+1)[/spoiler]
I'm not sure how to go from the second step to the third step. Can /sci/ help me out?

[Anonymous No.4248237]

You don't know the pythagorean theorem?

[Anonymous No.4248247]

1+1=2? Wow, who would have thought OP.

[Anonymous No.4248276]

I still don't get it.

[Anonymous No.4248282]

How do you not understand that the magnitude of a unit vector is 1?

[Anonymous No.4248287]

>>4248282
Oh, I forgot they were unit vectors. I am an idiot.

[EK !EKFQOBUFnQ No.4248289]

<span class="math">
\left \| \hat{x} \right \|^2 + \left \| \hat{y} \right \|^2 = 1
[/spoiler]
by the fucking pythagorean theorem

[Anonymous No.4248292]

>>4248289
Nope. That would give you 2xy + 1 and NOT 2(xy + 1) = 2xy + 2.

Welcome back, again, though. Going to behave this time? :)

[Anonymous No.4248300]

>>4248289
>HURR HOW DO I UNIT VECTOR

[Anonymous No.4248298]

>>4248289
Lulz?

[EK !EKFQOBUFnQ No.4248305]

>>4248292
OH noes, I dropped mai trip:
#.1Omhrk8
lolz I never even took this course yet, I just thought I would post arrogantly as EK and fuck all if i'm wrong

[Anonymous No.4248308]

>>4248289
lolololol

pic related

[EK !EKFQOBUFnQ No.4248309]

>>4248305
Wat?

[Anonymous No.4248315]

>>4248282
OP never said they were unit vectors.

[Anonymous No.4248318]

>>4248315
>doesn't know that a hat over a vector means its a unit vector

[Anonymous No.4248385]

>>4248228
those are unit vectors
this means they are equal to 1
x = 1; y = 1
(1+1)^2 = 1^2 + 2*1*1 + 1^2 = 2*1*1 + 2 = 2(1*1 + 1)

[Anonymous No.4248400]

>>4248385
>Implying <span class="math">\hat{x}\cdot \hat{y}=1[/spoiler]

<span class="math">||\hat{x}+\hat{y}||=2[/spoiler]. Look at the picture of the triangle above.

[Anonymous No.4248414]

>>4248400
it doesn't apply anything like what you say
and if it did it would be:
1^2 + 1^2 = 2^2