If ` vec a+ vec b+ vec c=0,| vec a|=3,| vec b|=5,| vec c|=7,` then find the angle between ` vec aa n d vec bdot`

Answer

`pi/3`

Explanation

`vec(a)+vec(b)=- vec(c) implies (vec(a)+vec(b)).(vec(a)+vec(b))=(-vec(c)).(-vec(c))`
`implies |vec(a)|^(2)+|vec(b)|^(2)+2 vec(a).vec(b)=|vec(c)|^(2) implies vec(a).vec(b)=15/2`
`implies ab cos theta = 15/2 implies (3xx5) cos theta =15/2 implies cos theta=1/2`.