If a, b, c are non-coplanar vectors and λ is a real number then [λ(a + b) λ^2b λc] = [a b + c b] for: - Mathematics MCQ AIEEE 2026 | ExamTest.live

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If a, b, c are non-coplanar vectors and λ is a real number then [λ (a + b) λ^{2} b λ c] = [a b + c b] for:

Solution & Step-by-step Explanation

Left Side: [λ (a + b) λ^{2} b λ c] = λ \cdot λ^{2} \cdot λ [(a + b) b c] = λ^{4} [(a + b) \cdot (b \times c)] = λ^{4} (a \cdot (b \times c) + b \cdot (b \times c)) = λ^{4} [a b c] .Right Side: [a b + c b] = a \cdot ((b + c) \times b) = a \cdot (b \times b + c \times b) = a \cdot (0 + c \times b) = [a c b] = - [a b c] .Equating LHS and RHS: λ^{4} [a b c] = - [a b c] Since a, b, c are non-coplanar, [a b c] \neq = 0 : λ^{4} = - 1 .A fourth power of a real number cannot be negative.Thus, no real value of λ exists.

Try it yourself before checking the explanation above.

If a, b, c are non-coplanar vectors and λ is a real number then [λ (a + b) λ^{2} b λ c] = [a b + c b] for:

exactly one value of λ

no value of λ

exactly three values of λ

exactly two values of λ

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