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Solution for The Xy-plane Divides the Line Joining the Points (−1, 3, 4) and (2, −5, 6) (A) Internally in the Ratio 2 : 3 (B) Externally in the Ratio 2 : 3 (C) Internally in the Ratio 3 : 2 - CBSE (Science) Class 12 - Mathematics

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Question

The xy-plane divides the line joining the points (−1, 3, 4) and (2, −5, 6)

  • internally in the ratio 2 : 3

  • externally in the ratio 2 : 3

  • internally in the ratio 3 : 2

  • externally in the ratio 3 : 2

Solution

\[\left( b \right) \text{ externally in the ratio 2: 3 } \]

\[\text{ Let the XY - plane divide the line segment joining points }P\left( - 1, 3, 4 \right) \text{ and } Q\left( 2, - 5, 6 \right) \text{ in the ratio k: 1 }. \]

\[\text { Using the section formula, the coordinates of the point of intersection are given by } \]

\[\left( \frac{k\left( 2 \right) - 1}{k + 1}, \frac{k\left( - 5 \right) + 3}{k + 1}, \frac{k\left( 6 \right) + 4}{k + 1} \right)\]

\[\text { On the XY - plane, the Z - coordinate of any point is zero } . \]

\[ \Rightarrow \frac{k\left( 6 \right) + 4}{k + 1} = 0\]

\[ \Rightarrow 6k + 4 = 0\]

\[ \Rightarrow k = - \frac{2}{3}\]

\[\text{ Thus, the XY - plane divides the line segment joining the given points in the ratio 2: 3 externally } . \]

 

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Solution The Xy-plane Divides the Line Joining the Points (−1, 3, 4) and (2, −5, 6) (A) Internally in the Ratio 2 : 3 (B) Externally in the Ratio 2 : 3 (C) Internally in the Ratio 3 : 2 Concept: Direction Cosines and Direction Ratios of a Line.
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