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Question
If `veca = vecb + vecc`, then is it true that `|veca| = |vecb| + |vecc|`? Justify your answer.
Solution
We have `veca = vecb + vecc`
∴ `|veca| = |vecb + vecc|`
Squaring, `|veca|^2 = |vecb + vecc|^2`
`= (vecb + vecc)* (vecb + vecc) = vecb .vecb + vecb.vecc + vecc .vecb + vecc.vecc`
`= |vecb|^2 + 2vecb * vecc + |vecc|^2` ...[∵ `vecb. vecc = vecc .vecb`]
`= |vecb|^2 + |vecc|^2 + 2 |vecb| |vecc| cos theta`
Where 'θ' is the angle between `vecb "and" vecc`
When θ = 0, then
`|veca|^2 = |vecb|^2 + |vecc|^2 + 2 |vecb| |vecc|`
`= (|vecb| + |vecc|)^2`
⇒ `|veca| = |vecb| + |vecc|.`
When θ ≠ 0, then `|veca| ne |vecb| + |vecc|`
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