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|^(2))^(2)`
`= | vec A| + | vec B|^(2)^(2) -2 | vec A ||vec B| 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 cos ^(2) theta//2)`
`=- 4 | vec A||vec B| cos^(2) theta//2)`
It is a negative quantity for all values of ` theta` and is zero value for ` theta=180^(@)`. Hence,
` | vec A-vec B| -lt |vec A|+|vec B|`