Math Is Fun Forum

GOKILL

Member

Registered: 2010-03-19

Posts: 26

Vec Vec Vector!!

1. Let

be non-zero vectors satisfying

. Suppose

are any numbers such that

. Prove that

---

I am the greatest magician this century!!!

rzaidan

Member

Registered: 2009-08-13

Posts: 59

Re: Vec Vec Vector!!

Hi GOKILL ;
you can take the dot product
(c1X1+c2X2+...c1X1).(c1X1+c2X2+...c1X1)=0  by using the associative and commutative properties,  and since each
Xi.Xj =0 for different i and j the product contains
the square of the constant times the square of the length of the corresponding vector , but this sum is zero , therefore each term is zero so each coefficient is zero so each ci is zero
Best Wishes
Riad Zaidan

Izmael

Member

Registered: 2010-03-28

Posts: 4

Re: Vec Vec Vector!!

Hi,

it will be much easier to take equation

Now, it is possible to multiply by x_j, so we have

Since 2-norm is always positive for nonzero vector x, we have c_j=0 for all j.