Let the co-ordinates of one vertex of \triangle {\ABC} be {\A}(0,2, \alpha) and the other two vertices lie on the line \frac{ {\x}+\alpha}{5}=\frac{ {\y}-1}{2}=\frac{z+4}{3}. For \alpha \in \mathbb{Z}, if the area of \triangle {\ABC} is 21 sq. units and the line segment {\BC} has length 2 \sqrt{21} units, then \alpha^2 is equal to _______. [29-Jan-2023 Shift 1]

JEE Mains 29-Jan-2023 Shift 1 Solved Paper

Section: Mathematics

Question : 81 of 90

Marks: +1, -0

Let the co-ordinates of one vertex of △ABC be A(0,2,α) and the other two vertices lie on the line ‌

x+α

=‌

y−1

=‌

z+4

. For α∈ℤ, if the area of △ABC is 21 sq. units and the line segment BC has length 2√21 units, then α2 is equal to _______.

[29-Jan-2023 Shift 1]

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