Let the coordinates of one vertex of triangle ABC be A(0, 2, α) a… | JEE Main 2023 Mathematics PYQ

MCQMediumJEE Main 2023 · 29 January, Shift 1Cross Product

Let the coordinates 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 $21$ square units and the line segment BC has length $2\sqrt{21}$ units, then $\alpha^2$ is equal to:

A
$9$
B
$16$
C
$25$
D
$36$

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