Shortest distance between lines r-5i-7j-3k- 5i-16j-7k and r-9i-13j-15k- 3i-8j-5k-

The correct option is D None of these r⃗=a⃗_1+λb⃗_1 a⃗=5i 7j+3k b⃗_1=5i 16j+7k and from r⃗=a⃗_2+λ b_2 a⃗_2=9i+13j+15k b⃗_2=3i+8j 5 ...

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Perpendicular Distance of a Point from a Plane

Shortest dist...

Question

Shortest distance between lines
$\to r = (5 i + 7 j + 3 k) + λ (5 i - 16 j + 7 k)$ and $\to r = (9 i + 13 j + 15 k) + μ (3 i + 8 j - 5 k) :$

10

unit

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12

unit

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14

unit

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None of these

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Find the shortest distance between lines

and.

\vec{r} = 3 \hat{i} + 8 \hat{j} + 3 \hat{k} + λ (3 \hat{i} - \hat{j} + \hat{k}) and \vec{r} = - 3 \hat{i} - 7 \hat{j} + 6 \hat{k} + μ (- 3 \hat{i} + 2 \hat{j} + 4 \hat{k})

\vec{r} = (3 \hat{i} + 5 \hat{j} + 7 \hat{k}) + λ (\hat{i} - 2 \hat{j} + 7 \hat{k}) and \vec{r} = - \hat{i} - \hat{j} - \hat{k} + μ (7 \hat{i} - 6 \hat{j} + \hat{k})

\vec{r} = (\hat{i} + 2 \hat{j} + 3 \hat{k}) + λ (2 \hat{i} + 3 \hat{j} + 4 \hat{k}) and \vec{r} = (2 \hat{i} + 4 \hat{j} + 5 \hat{k}) + μ (3 \hat{i} + 4 \hat{j} + 5 \hat{k})

\vec{r} = (1 - t) \hat{i} + (t - 2) \hat{j} + (3 - t) \hat{k} and \vec{r} = (s + 1) \hat{i} + (2 s - 1) \hat{j} - (2 s + 1) \hat{k}

\vec{r} = (λ - 1) \hat{i} + (λ + 1) \hat{j} - (1 + λ) \hat{k} and \vec{r} = (1 - μ) \hat{i} + (2 μ - 1) \hat{j} + (μ + 2) \hat{k}

\vec{r} = (2 \hat{i} - \hat{j} - \hat{k}) + λ (2 \hat{i} - 5 \hat{j} + 2 \hat{k}) and, \vec{r} = (\hat{i} + 2 \hat{j} + \hat{k}) + μ (\hat{i} - \hat{j} + \hat{k})

\vec{r} = (\hat{i} + \hat{j}) + λ (2 \hat{i} - \hat{j} + \hat{k}) and, \vec{r} = 2 \hat{i} + \hat{j} - \hat{k} + μ (3 \hat{i} - 5 \hat{j} + 2 \hat{k})

\vec{r} = (8 + 3 λ) \hat{i} - (9 + 16 λ) \hat{j} + (10 + 7 λ) \hat{k}

\vec{r} = 15 \hat{i} + 29 \hat{j} + 5 \hat{k} + μ (3 \hat{i} + 8 \hat{j} - 5 \hat{k})

\to r = 6^i + 2^j + 2^k + λ (^i - 2^j + 2^k)

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

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

\to r =^2 i -^j -^k + μ (^2 i +^j + 2^k)

\to r = (3 i + 8 j + 3 k) + λ (3 i - j + k)

\to r = (- 3 i - 7 j + 6 k) + μ (- 3 i + 2 j + 4 k)

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