If the components of a = i + j + k along and perpendicular to b =3 i + j - k respectively, are 16 11 (3 i + j - k ) and 1 11 (-4 i -5 j -17 k ) , then ^2+ ^2+ ^2 is equal to :

Step-by-step solution

let a ₁₁= component of a along b a ₁= component of a perpendicular to b aligned & a ₁₁= 16 11 (3 i + j - k ) & a ₁= 1 11 (-4 i -5 j -17 k ) & a = a ₁₁+ a ₁ aligned aligned & array l a = = 16 11 (3 i + j - k )+ 1 11 (-4 i -5 j -17 k ) 11 j - 33 11 k array & aligned =4 i + j -3 k aligned & ^2+ ^2+ ^2=16+1+9=26 aligned