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## Homework Statement

if vectors [tex]\vec{a}[/tex] and [tex]\vec{b}[/tex] have opposite directions, how to show that |[tex]\vec{a}[/tex]| + |[tex]\vec{b}[/tex]| = |[tex]\vec{a}[/tex] - [tex]\vec{b}[/tex]|?

## Homework Equations

quadratic equation, definition of absolute value

## The Attempt at a Solution

[tex]|\vec{a}-\vec{b}| = \sqrt{\vec{a}^{2}-2\vec{a}\bullet\vec{b}+\vec{b}^{2}}[/tex]

and then I got

[tex]|\vec{a}-\vec{b}| = \sqrt{\vec{a}^{2}-2|\vec{a}||\vec{b}|cos\Phi+\vec{b}^{2}}[/tex]

So then cosine of the angle is equal to -1, and I don't know how to go from there.

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