Question

Can we apply Pythagoras theorem in vectors.......???
Why can we do this despite they are vectors not lenghts.....???​

Answer 1

Explanation:

i don't think we use Pythagoras Theron

but if asked we has To use

Answer 2

The user @SkG noted that it should be an answer rather than a comment.

Let △ABC be some arbitrary triangle with sides a,b,c (assume that AB=a,BC=b,AC=c) such that

a2+b2=c2(1)

We can construct △DEF which is right angled and has sides a,b,d (assume DE=a,EF=b,DF=d) such that d is length of the hypotenuse, i.e ∠DEF=90∘. By Pythagorean theorem we have

a2+b2=d2(2)

Now we can put (1) in (2) and get c2=d2. c,d>0, hence c=d.

We can use SSS to claim that △ABC≅△DEF, so ∠ABC=∠DEF=90∘, hence △ABC is right angled.

Q.E.D