How can I use the dot product formula to find the angle between two vectors?

[leitz]

Homework Statement

Prove : ||V - U|| => | ||V||-||U|| |
V and U are vectors

Homework Equations

Maybe the dot product formula: ||A||*||B||cosθ

The Attempt at a Solution

==> ||V - U||² >= (||V||-||U||)²
==> (V-U) . (V-U) >= ||V||² +||U||² - 2||U||*||V||
==> V.V + U.U -2U.V >= V.V + U.U - 2||U||*||V||
==> -2U . V >= -2 ||U||*||V||

I don't know how to go on from here. I always get a nonsensical answer if I try to simplify this. Am I using the right approach?

 

[LCKurtz]

Homework Statement

Prove : ||V - U|| <= | ||V||-||U|| |
V and U are vectors

Homework Equations

Maybe the dot product formula: ||A||*||B||cosθ

You have the inequality backwards above.

Hint: ||u|| = ||(u - v) + v|| ≤ ...

 

[leitz]

Can you give me another hint please?

 

[LCKurtz]

You have the inequality backwards above.

Hint: ||u|| = ||(u - v) + v|| ≤ ...

Can you give me another hint please?

What did you try with my hint? What might go after the ≤ ?