Let L1 be the line r1 - 2i- - j- - k- - - i- - 2k- and L2 be the line r2 - 3i- - j- - - i- - j- - k- Let - be the plane which contains the L1 and is parallel to L2- The distance of the plane - from the origin is

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Direction Cosines

Let L1 be t...

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Let $L_{1}$ be the line $r_{1} = 2 \to i + \to j - \to k + λ (\to i + 2 \to k)$ and $L_{2}$ be the line $r_{2} = 3 \to i + \to j + μ (\to i + \to j - \to k)$ . Let $π$ be the plane which contains the $L_{1}$ and is parallel to $L_{2}$ . The distance of the plane $π$ from the origin is

1.7

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\frac{\sqrt{2}}{\sqrt{7}}

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\sqrt{6}

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None of these

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L_{1}

{\to r}_{1} = 2 \to i + \to j - \to k + λ (\to i + 2 \to k)

L_{2}

{\to r}_{2} = 3 \to i + \to j + μ (\to i + \to j - \to k)

π

L_{1}

L_{2}

π

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

l_{1} = \to r (t) = (\to i - 6 \to j + 2 \to k) + t (\to i + 2 \to j + \to k)

l_{2} = \to R (u) = (4 \to j + \to k) + u (2 \to i + \to j + 2 \to k)

A

P_{1}

P_{2}

P_{1}

2 \to j + 3 \to k

4 \to j - 3 \to k

P_{2}

\to j - \to k

3 \to i + 3 \to j

A

2 \to i + \to j - 2 \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

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