Let v ₁= i -2 j +a k , v ₂ =2 i + j - k and v ₃= i + k be three vectors such that the value of ' a ' is maximum for v ₁ v ₂=0 where [0, ] . If for these values of ' a ' and ' ' = p q where p, q N , then find least value of |p-4 q|

Step-by-step solution

aligned & v ₁ v ₂ =0 2 -2 -a=0 a=2( - ) & .a |_ max. =2 2 when =3 / 4 aligned = [ array lll v ₁ & v ₂ & v ₃ array ] aligned [ array lll v₁ & v ₂ & v ₃ array ]= | array ccc 1 / 2 & -2 & 2 2 2 & -1 / 2 & -1 1 & 0 & 1 array |=1(2+2)+1 ( -1 2 +4 )= 15 2 = p q |p-4 q|=|15-8|=7 aligned