1.

Prove that : |veca + vecb|le|veca|+|vecb|.

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Solution :
Let ABC be the triangle where `vec(AB) = VECA. vec(BC) = vecb`
Then `vec(AC) = veca=vecb`
Now `|veca| = AB, |vecb| = BC` and `|veca+vecb| = AC`
In the triangle ABC,
`AC `implies |veca+vecb|<|veca|+|vecb|`
Now AC = AB+BC when A,B,C LIE on a straight line A,B,C are collinear.
Hence `|veca+vecb| = |veca|+|vecb|`
When `veca` and `vecb` are like collinear vectors or ZERO vectors.


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