If the lines 2 x − 1 = x 1 y − 2 = x 2 z − 3 and 3 x − 2 = 4 y − 3 = 5 z − 4 lie in the same plane, then for the equation x 1 t 2 + ( x 2 + 2 ) t + a = 0

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Mathematics - 3D Coordinate Geometry Question with Solution | TestHub

Mathematics3D Coordinate GeometryCoplanarity of two linesMedium2 minQB

MathematicsMediummultiple choice

If the lines $\frac{x - 1}{2} = \frac{y - 2}{x _{1}} = \frac{z - 3}{x _{2}}$ and $\frac{x - 2}{3} = \frac{y - 3}{4} = \frac{z - 4}{5}$ lie in the same plane, then for the equation $x_{1} t^{2} + (x_{2} + 2) t + a = 0$

Options:(select one or more)

Answer:

A, B

Solution:

Coplanarity: the determinant with rows $(1, 1, 1), (2, x_{1}, x_{2}), (3, 4, 5)$ must be zero, which gives $2 x_{1} - x_{2} = 2$ . Then $x_{2} + 2 = 2 x_{1}$ , so the equation is $x_{1} t^{2} + 2 x_{1} t + a = 0$ and the sum of its roots is -2.

Stream:JEESubject:MathematicsTopic:3D Coordinate GeometrySubtopic:Coplanarity of two lines

⏱ 2mℹ️ Source: QB

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