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3D Geometry question

2023 · 29 Jan · Shift 1 · Q48

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JEE Main
Mathematics
3D Geometry
2023 · 29 Jan · Shift 1 · Q48

3D Geometry question

2023 · 29 Jan · Shift 1 · Q48

JEE MainMathematics3D GeometryNumerical+4 / −1

Let the co-ordinates of one vertex of

\Delta ABC

be

A(0,2,\alpha)

and the other two vertices lie on the line

{{x + \alpha } \over 5} = {{y - 1} \over 2} = {{z + 4} \over 3}

. For

\alpha \in \mathbb{Z}

, if the area of

\Delta ABC

is 21 sq. units and the line segment

BC

has length

2\sqrt{21}

units, then

\alpha^2

is equal to

\underline{\hspace{2cm}}

.

Numerical answer

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