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## Homework Statement

__A.__

Given unit vectors

**a**,

**b**,

**c**in the x, y-plane such that

**a · b**=

**b · c**= 0,

let

**v**=

**a**+

**b**+

**c**; what are the possible values of |

**v**|?

__B.__

Repeat, except

**a**,

**b**, and

**c**are unit vectors in 3-space

## Homework Equations

## The Attempt at a Solution

I have solutions for both that I'm reasonably sure of, I'd just like a 2nd opinion to make sure I solved the problem correctly.

For part A I got |

**v**| = [itex]\sqrt{2}[/itex], [itex]\sqrt{5}[/itex]

I took

**c**= <0,1>,

**a**= <1,0>

**b**= <0,1> in this combination |

**v**| = [itex]\sqrt{2}[/itex].

The only other special case is when

**a**=

**b**in this case, |

**v**| = [itex]\sqrt{5}[/itex]

For Part B I took

**c**= <0,0,1>,

**a**= <1,0,0> and

**b**= [itex]<cos\theta,sin\theta,0>[/itex]

Therefore, |

**v**| = [itex]\sqrt{2cos\theta + 3}[/itex], [itex]0\leq\theta\leq 2\pi[/itex]