Posted by **chris** on Monday, July 16, 2007 at 5:44pm.

show that if u (dot) v = 0 for all vectors v, then u = 0.

One of the Axioms an inner product has to satisfy is:

x dot x >=0 where equality only holds if x = 0

So, in your problem you take the special case v = u. Then:

u dot u = 0 ---->

u = 0

## Answer this Question

## Related Questions

- Vectors: Dot product - Given a and b unit vectors if |a+b|=square root 3, ...
- Vectprs and Scalars - Why are some of these scalars and others are vectors? What...
- linear algebra - show that if u dot v = u dot w for all u, then v = w. You can ...
- Math - Vectors - If "u = (2,2,-1)", "v = (3,-1,0)" and "w = (1,7,8)", verify ...
- Math - Product Dot Vectors - How would you expand and simplify the following ...
- Linear Algebra - Let u and v be vectors in R^n, and let T be a linear operator ...
- linear algebra compute vectors - ||u||=2 ||v||=3 ||w||=5 u dot v = -1 u dot w = ...
- dot product of vecotrs - Question: Find (3a+b)dot(2b-4a) if a=-i-3j+k and b=2i+...
- Algebra - Hi, I'm struggling to do two questions. 1) If ||u||=2, ||v||=root 3 ...
- Calculus - Two force vectors act on an object and the dot product of the two ...

More Related Questions