JEE Advanced 2019 Paper 1 Mathematics Q18

Mathematics

Problem

Three lines are given by

\vec{r}

= λî, λ ∈ ℝ;

\vec{r}

= μ(î + ĵ), μ ∈ ℝ; and

\vec{r}

= ν(î + ĵ +

\hat{k}

), ν ∈ ℝ. Let the lines cut the plane x + y + z = 1 at the points A, B and C respectively. If the area of the triangle ABC is Δ then the value of (6Δ)² equals _____.

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