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For any two vectors vec aa n d vec b , ...

For any two vectors ` vec aa n d vec b` , prove that `| vec a+ vec b|lt=| vec a|+| vec b|` (ii) `| vec a- vec b|lt=| vec a|+| vec b|` (iii) `| vec a- vec b|geq| vec a|-| vec b|`

Text Solution

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`|veca+vecb|^2 = |veca|^2 + |vecb|^2 +2|veca||vecb| costheta`
`|veca+vecb|^2 = |veca|^2 + |vecb|^2 +2|veca||vecb|` [since , `-1 <=costheta <= 1`]
Now , `2|veca||vecb| costheta <= 2|veca||vecb|`
so,
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