- #1

- 10

- 0

## Homework Statement

*

**v**and

**u**are vectors where ||

**u**|| is the magnitude of

**u**and ||

**v**|| is the magnitude of

**v**

Prove that ||

**u**+

**v**|| = ||

**u**|| + ||

**v**|| if and only if

**u**and

**v**have the same direction.

## Homework Equations

## The Attempt at a Solution

At first, I tried using what it means for two vectors to have the same direction:

**u**=

**v**/||

**v**||

**u**+

**v**=

**v**/||

**v**|| +

**v**(added

**v**to both sides)

||

**u**+

**v**|| = ||(

**v**/||

**v**||) +

**v**|| (took the magnitude of both sides)

From here, if I substitute (

**v**/||

**v**||) with

**u**, I would just have ||

**u**+

**v**|| equal to itself.

I also tried looking up Properties of Dot Product but couldn't find a place to apply them. I'm kinda stuck on what else I can do so if anyone can provide tips or pointers in the right direction, I'd be grateful.