Is ` | vec A + vec B|` greater than or less than ` |vec A| + |vec B| `? Explain.

Explanation

` | vec A + vec B^(2)| -(| vec A | + |vec B| + |vec B|)^(2)`
`= | vec A|^(2) + |vec B|^(2) + | vec A| |verc AB| cos theta`
`- | vec A|^(2) - | vec B | ^(2) - 2 |vec A | |vec B|`
`=- 2 | vec A | | vec B| (1- cos theta )`
` =- 2 | vec A| | vec B| (2 sin ^(2) theta//2)`
`=- 4 | vec A | |vec B| sin^(2) theta//2`
It is a negative quantity for all values of `theta` and is
zero if ` theta=0^(@)`. Hence, ` | vec A + vec B| -lt | vec A|+| vec B|`.