Let →a = 2î + λ₁ĵ + 3k̂, →b = 4î + (3 − λ₂)ĵ + 6k̂ and →c = 3î + 6ĵ + (λ₃)k̂ be three vectors such that →b = 2→a and →a is perpendicular to →c. Then a possible value of (λ₁, λ₂, λ₃) is?

→b = 2→a ⇒ 4î + (3 − λ₂)ĵ + 6k̂ = 4î + 2λ₁ĵ + 6k̂ ⇒ 3 − λ₂ = 2λ₁ ⇒ 2λ₁ + λ₂ = 3 (1)
Given →a ⋅ →c = 0 ⇒ 6 + 6λ₁ + 3(λ₃) = 0 ⇒ 2λ₁ + λ₃ = −2 .. (2)
Now (λ₁, λ₂, λ₃) = (λ₁, 3 − 2λ₁, −2 − 2λ₁)
putting λ₁ = −2 ⇒ (−2, 4, 0)
Now check the options, option (4) is correct.