Mathematics - 3D-Coordinate Geometry Question with Solution | TestHub

Mathematics3D-Coordinate GeometryCoordinates of a point in space, Direction cosines,Easy2 minPYQ_2023

MathematicsEasysingle choice

The ratio in which the YZ-plane divide the line segment formed by joining the points $(- 2, 4, 7)$ and $(3, - 5, 8)$ is $2 : m$ . The value of $m$ is

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Answer:

Solution:

Let the points be $A (- 2, 4, 7)$ and $B (3, - 5, 8)$ on $Y Z$ -plane, $x$ -coordinate $= 0$ .

Let the ratio be $K : 1$ .
The coordinates of $C$ are $(\frac{3 K - 2}{K + 1}, \frac{- 5 K + 4}{K + 1}, \frac{8 K + 7}{K + 1})$
Clearly $\frac{3 K - 2}{K + 1} = 0 \Rightarrow 3 K = 2 \Rightarrow K = \frac{2}{3}$
Hence required ratio is $2 : 3$ .

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

⏱ 2mℹ️ Source: PYQ_2023

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