If the median through A of △ A BC having vertices A ≡ ( 2 , 3 , 5 ) , B ≡ ( − 1 , 3 , 2 ) and C ≡ ( λ , 5 , μ ) is equally inclined to the axes, then

The mid-point of BC is ( 2 λ − 1 , 4 , 2 μ + 2 ) . Direction ratios of the median: ( 2 λ − 5 , 1 , 2 μ − 8 ) . For equal inclination the direction ratios are equal: 2 λ − 5 = 1 = 2 μ − 8 , so λ = 7 , μ = 10 .

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Mathematics - 3D Coordinate Geometry Question with Solution | TestHub

Mathematics3D Coordinate GeometryCoordinates of a point in space, Direction cosines,Medium2 minQB

MathematicsMediummultiple choice

If the median through $A$ of $△ A BC$ having vertices $A \equiv (2, 3, 5), B \equiv (- 1, 3, 2)$ and $C \equiv (λ, 5, μ)$ is equally inclined to the axes, then

Options:(select one or more)

Answer:

A, B

Solution:

The mid-point of $BC$ is $(\frac{λ - 1}{2}, 4, \frac{μ + 2}{2})$ . Direction ratios of the median: $(\frac{λ - 5}{2}, 1, \frac{μ - 8}{2})$ . For equal inclination the direction ratios are equal: $\frac{λ - 5}{2} = 1 = \frac{μ - 8}{2}$ , so $λ = 7, μ = 10$ .

Stream:JEESubject:MathematicsTopic:3D Coordinate GeometrySubtopic:Coordinates of a point in space, Direction cosines,

⏱ 2mℹ️ Source: QB

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