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Mathematics - Vector Question with Solution | TestHub

MathematicsVectorMiscellaneous/MixedMedium2 minQB

MathematicsMediumnumerical

Nonzero real numbers $α, β, γ, x, y, z$ satisfy $αx + β y + γ z + (α^{2} + β^{2} + γ^{2}) (x^{2} + y^{2} + z^{2}) = 0$ . Find $\frac{α y}{x β} + \frac{β z}{y γ}$ .

Answer:

2.00

Solution:

Equality in Cauchy implies $(α, β, γ)$ and $(x, y, z)$ are antiparallel and proportional. Each ratio equals 1, so the sum is 2.

Stream:JEESubject:MathematicsTopic:VectorSubtopic:Miscellaneous/Mixed

⏱ 2mℹ️ Source: QB

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