If `veca+vecb+vecc` = `vec0, |veca|` = 3 , `|vecb|` = 5 and `|vecc|` = 7, find the angle between `veca` and `vecb`.

Explanation

`veca+vecb+vecc` = 0
`implies veca+vecb` = `-vecc`
`implies (veca+vecb)^2` = `(-vecc)^2
`implies |veca|^2+|vecb|^2+2veca.vecb` = `|vecc|^2`
`implies 9+25+2veca.vecb` = 49
`implies 2veca.vecb` = 49-34 = 15
`implies 2|veca||vecb|costheta` = 15 (where `theta` is the angle between `veca` and `vecb`)
`implies costheta` = 15/(2.3.5) = 1/2
`implies theta` = `pi/3`