The ratio in which the plane r- i-2j-3k-17 divides the line joining the points -2i-4j-7k- and 3i-5j-8k- is-

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Section Formula

The ratio in ...

Question

The ratio in which the plane $\to r \cdot (\to i - 2 \to j + 3 \to k) = 17$ divides the line joining the points $- 2 \to i + 4 \to j + 7 \to k$ and $3 \to i - 5 \to j + 8 \to k$ is-

1 : 5

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1 : 10

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3 : 5

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3 : 10

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Solution

The correct option is D $3 : 10$
Equation of plane in cartesian form is, $x - 2 y + 3 z - 17 = 0$ ..... $(1)$
Assume this plane $(1)$ divide the line segment joining the points $(- 2, 4, 7)$ and $(3, - 5, 8)$ in $m : n$ ratio
Therefore, $\frac{m}{n} = \frac{- 2 - 2 (4) + 3 (7) - 17}{3 - 2 (- 5) + 3 (8) - 17} = \frac{- 3}{10} < 0$
Hence, plane (1) divides the given line segment externally $3 : 10$

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The ratio in which the plane →r⋅(→i−2→j+3→k)=17 divides the line joining the points −2→i+4→j+7→k and 3→i−5→j+8→k is-

The ratio in which the plane $\to r \cdot (\to i - 2 \to j + 3 \to k) = 17$ divides the line joining the points $- 2 \to i + 4 \to j + 7 \to k$ and $3 \to i - 5 \to j + 8 \to k$ is-