SATHEE: 3D Geometry 3 Question 57

3D Geometry 3 Question 57

####57. The shortest distance between $L_{1}$ and $L_{2}$ is

(a) 0 unit

(b) $17 / \sqrt{3}$ units

(c) $41 / 5 \sqrt{3}$ unit

(d) $17 / 5 \sqrt{3}$ units

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Answer:

Correct Answer: 57. (d)

Solution:

The shortest distance between $L_{1}$ and $L_{2}$ is

$\begin{aligned} | \frac{(2 - (- 1)) \hat{i} + (2 - 2) \hat{j} + (3 - (- 1)) \hat{k} \cdot (\hat{i} - 7 \hat{j} + 5 \hat{k})}{5 \sqrt{3}} | \\ = | \frac{(3 \hat{i} + 4 \hat{k}) \cdot (\hat{i} - 7 \hat{j} + 5 \hat{k})}{5 \sqrt{3}} | \\ = \frac{17}{5 \sqrt{3}} units \end{aligned}$

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