If M₁, M₂, M₃ and M₄ , are respectively the magnitudes of the vectors a ₁=2 i - j + k , a ₂=-3 i -4 j -4 k , a ₃=- i + j - k , a ₄=- i +3 j + k , then the correct order of M₁, M₂, M₃ and M₄ is

Step-by-step solution

Given that, a₁=2 i - j + k aligned & a₂=3 i -4 j -4 k & a₃=- i + j - k & a₄=- i +3 j + k aligned As M₁, M₂, M₃ and M₄ are the magnitudes of the vectors a ₁, a ₂, a ₃ and a ₄ respectively. aligned & M₁= | a ₁ | & = (2)^2+(-1)^2+(1)^2 & = 4+1+1 = 6 & M₂= | a ₂ | & = (3)^2+(-4)^2+(-4)^2 & = 9+16+16 = 41 & M₃= | a ₃ | & = (-1)^2+(1)^2+(-1)^2 & = 1+1+1 = 3 & M₄= | a ₄ | aligned aligned & = (-1)^2+(3)^2+(-1)^2 & = 1+9+1 = 11 aligned Hence, the correct order of magnitudes M₃ < M₁ < M₄ < M₂