A vector A when added to the sum of the vectors ( i - 2 j + 2 k ) and (-2 i + j - k ) gives a unit vector along Y axis. The magnitude of vector A is

Step-by-step solution

Let the given vectors be V ₁ = i - 2 j + 2 k and V ₂ = -2 i + j - k . The sum of these vectors is V ₁ + V ₂ = - i - j + k . According to the given condition, A + ( V ₁ + V ₂) = j . Substituting the sum, we get A + (- i - j + k ) = j . A = j - (- i - j + k ) = i + 2 j - k . The magnitude of vector A is | A | = 1^2 + 2^2 + (-1)^2 = 6 . Answer: 6