If (a+b). (a-b) = 8 and |a| = 8 |b|, then the values of |a| and |b| are

Options

A. `(16)/(3)sqrt((2)/(7)), (2)/(3)sqrt((2)/(7))`
B. `(4)/(3)sqrt((2)/(7)),(2)/(3)sqrt((3)/(7))`
C. `(12)/(5)sqrt((2)/(7)),(4)/(3)sqrt((2)/(7))`
D. None of these

Answer

A

Explanation

Given ,`(a+b).(a-b)=8 and |a|=8 |b| `
`implies a.a-a.b+b.a-b.b=8`
`implies |a|^(2)-|b|^(2)=8[ :' a.a=|a|^(2)and a.b=b.a]`
`implies (8|b|)^(2)-|b|^(2)=8`
`= 63|b|^(2)=8`
`implies |b|= sqrt((8)/(63))=(2)/(3) sqrt((2)/(7))`
Also ,`|a|=8|b|=8((2)/(3)sqrt((2)/(7)))=(16)/(3)sqrt((2)/(7))`