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Is | \(\vec a-\vec b\) | greater than or less than | \(\vec a\) | + | \(\vec b\) |?

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\({|\vec a-\vec b|}^2-{(|\vec a|+|\vec b|)}^2\)

\(|\vec a|^2+|\vec b|^2-2\,|\vec a|\,|\vec b|\,cos\, \theta-|\vec a|^2-|\vec b|^2-2|\vec a||\vec b|\)

⇒-4| a | | b | \(cos^2\frac{\theta}{2}\)

= a negative quantity

Hence,  \(|\vec a- \vec b|<|\vec a|+|\vec b|\)

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