Find `|vec(a)| and |vec(b)|`, if `(vec(a)+vec(b)).(vec(a)-vec(b))=8 and |vec(a)|=8|vec(b)|`.

Explanation

Given , `(vec(a)+vec(b)).(vec(a)-vec(b))=8 and |vec(a)|=8 |vec(b)|`.
`rArr vec(a).vec(a_2)-vec(a).vec(b)+vec(b).vec(a)-vec(b).vec(b)=8`.
`rArr |vec(a)|^2-|vec(b)|^2=8`
`rArr (8|b|)^2-|b|^2 =8 rArr 63 |b|^2=8`.
`rArr |vec(b)|=sqrt((8)/(63))=(2)/(3)sqrt((2)/(7))`.
Also , `|vec(a)|=8|vec(b)|=8 ((2)/(3)sqrt((2)/(7)))=(16)/(3)sqrt((2)/(7))`.