If ` vec a\ a n d\ vec b` are two non collinear unit vectors such that `| vec a+ vec b|=3,\ `find`\ (2 vec a-5 vec b)dot(3 vec a+ vec b)dot`

Explanation

Given that,
` vec a\ a n d\ vec b`
are two non collinear unit vectors.
`=>|vec a|=| vec b|=1`
given` | vec a+ vec b|=3`
`=>| vec a+ vec b|^2=9`
`=>(vec a+ vec b)*(vec a+ vec b)=9`
`=|vec a|^2+2 (vec a vec b)+|vec b|^2=9`
`=>2 (vec a vec b)=9-2`
`vec a vec b=7/2`
` (2 vec a-5 vec b)*(3 vec a+ vec b)`
`=6+2 vec a vec b -15 vec a vec b -5`
`=1-13vec a vec b`
`=1-13 xx 7/2`
`=(2-91)/2`
`=-89/2`