Find `| vec a|a n d\ | vec b|` , if : `( vec a+ vec b)dot( vec a- vec b)=8\ a n d\ | vec a|=8| vec b|`

Answer

`|vec(a)|=8 sqrt(8/63)` and `|vec(b)|=sqrt(8/63)`

Explanation

`|vec(a)|^(2)-|vec(b)|^(2)=8implies 64 |vec(b)|^(2)-|vec(b)|^(2)=8 implies |vec(b)|^(2)=8/63`
`:. |vec(b)|=sqrt(8/63)` and `|vec(a)|=8.sqrt(8/63)`.