Let the position vectors of the points A, B, C and D be 5 i+5 j+2 λ k, i+2 j+3 k,-2 i+λ j+4 k and -i+5 j+6 k. Let the set S=\λ R: the points A, B, C and D are coplanar. Then Σ λ S (λ+2)² is equal to:

Vector Algebra: JEE Main 2023 Mathematics question

JEE Main 2023 · 6 Apr, Morning shift · Q5752

JEE Main 20236 Apr, Morning shiftMathematicsHardVector Algebra184× since 2002

Let the position vectors of the points A, B, C and D be

5 \hat{i}+5 \hat{j}+2 \lambda \hat{k}, \hat{i}+2 \hat{j}+3 \hat{k},-2 \hat{i}+\lambda \hat{j}+4 \hat{k}

and

-\hat{i}+5 \hat{j}+6 \hat{k}

. Let the set

S=\{\lambda \in \mathbb{R}

: the points A, B, C and D are coplanar

\}

. Then

\sum_\limits{\lambda \in S}(\lambda+2)^{2}

is equal to :