i know how to prove it i think...
but i dont understand what the professor means by this @ganeshie8
||V+W||^2
= ||V||^2 + ||W||^2 + 2V*W

(less than or equal to) ||V||^2 +||W||^2 +2||v||*||W||

= (||V|| + ||W||)^2

taking sqr
||V+W|| (less than or equal to) ||V||+||W||

Question

i know how to prove it i think...
but i dont understand what the professor means by this @ganeshie8 
||V+W||^2
= ||V||^2 + ||W||^2 + 2V*W

(less than or equal to) ||V||^2 +||W||^2 +2||v||*||W||

= (||V|| + ||W||)^2

taking sqr
||V+W|| (less than or equal to) ||V||+||W||

anonymous · Answer

like i get how it equals the first  and second "line" 
but then i dont get how he jumps to the final line
like what happened to the +2||V||||W|| ?

ganeshie8 · Answer

$$V\bullet W = \|V\| \|W\| \cos\theta   $$

ganeshie8 · Answer

would you agree  $V\bullet W \le \|V\| \|W\|    $ ?

anonymous · Answer

yes

ganeshie8 · Answer

good

anonymous · Answer

but how does that get into this "proof"?

ganeshie8 · Answer

so you agree that

$||V+W||^2 \le  ||V||^2 +||W||^2 +2||v||*||W||$


?

anonymous · Answer

yeah

ganeshie8 · Answer

right hand side can be written as  (||V|| + ||W||)^2
so thats same as

$||V+W||^2 \le  (||V|| + ||W||)^2$

yes ?

anonymous · Answer

ok wait hold on... lol let me try to process it ._.

ganeshie8 · Answer

recall the formula $$\heartsuit^2+\spadesuit^2 + 2\heartsuit \spadesuit  = (\heartsuit + \spadesuit)^2$$

anonymous · Answer

So i think i get. i got:
||V||^2 + ||W||^2 + 2V*W (less than or equal to) ||V||^2 + ||W||^2 + 2||V||||W||
so simply because 2V*W (less than or equal to) 2||V||||W||
it validates the upper equation, am i right?

ganeshie8 · Answer

Exactly!

anonymous · Answer

oh ok. so why after did he put...

= (||V|| + ||W||) ^2
taking sqrt you get the answer

like coming from MY equation how would taking the sqrt get to the answer? I just stopped there because i justified it but i never ended up back to 
||V+W|| (less than or equal to) ||V||+||W||

ganeshie8 · Answer

$$||V+W||^2 \le  (||V|| + ||W||)^2$$

are you okays  up to this step ?

anonymous · Answer

like i GET how it proves the inequality but how did he get rid of the 2V*W on the left side and 2||V||||W|| on the right to finally get ||V+W|| <or= ||V||+||W||

ganeshie8 · Answer

||V+W||^2   =    ||V||^2 + ||W||^2 + 2V*W
                  <=  ||V||^2 + ||W||^2 + 2||V||||W ||
                  <= (||V|| + ||W||)^2

ganeshie8 · Answer

Notice that the left side is always ||V+W||^2
your prof is only messing witht he right hand side

anonymous · Answer

oh *palm to the face* ughhh 
thank you for being so patient with me :)
i get it. ._.

ganeshie8 · Answer

haha np:)