The distance between the plane whose equation is r- 2i-j-3k-5 and the line whose equation is r-i- 2i-5j-3k-is

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Equation of a Plane : Intercept Form

The distance ...

Question

The distance between the plane whose equation is $\to r \cdot (2 \to i + \to j - 3 \to k) = 5$ and the line whose equation is $\to r = \to i + λ (2 \to i + 5 \to j + 3 \to k)$ ,is

\frac{3}{\sqrt{14}}

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\frac{5}{\sqrt{14}}

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5

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0

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Solution

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Similar questions

\to r = 2 \to i - 2 \to j + 3 \to k + λ (\to i - \to j + 4 \to k)

\to r \cdot (\to i + 5 \to j + \to k) = 5

\to r = (- \to i + 2 \to j + 3 \to k) + t (- 2 \to i + \to j + \to k)

\to r = (2 \to i + 3 \to j + 5 \to k) + s (\to i + 2 \to j + 3 \to k)

\to r = \to i + 2 \to j + 3 \to k + λ (\to i - \to j + \to k) a n d \to r = 2 \to i - \to j - \to k + μ (\to - i + \to j - \to k) i s

The lines $\to r = \to i - \to j + λ (2 \to i + \to k)$ and $\to r = (2 \to i - \to j) + μ (\to i + \to j - \to k)$ intersect for

\to r = 3 \to i + 2 \to j - 5 \to k

\to a = 2 \to i - \to j + \to k

\to b = \to i + 3 \to j - 2 \to k

\to c = - 2 \to i + \to j - 3 \to k

\to r = λ \to a + μ \to b + ν \to c

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