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
Show Answer
Answer:
Correct Answer: 57. (d)
Solution:
- The shortest distance between $L_{1}$ and $L_{2}$ is
$ \begin{aligned} & \left|\frac{{(2-(-1)) \hat{\mathbf{i}}+(2-2) \hat{\mathbf{j}}+(3-(-1)) \hat{\mathbf{k}}} \cdot(\hat{\mathbf{i}}-7 \hat{\mathbf{j}}+5 \hat{\mathbf{k}})}{5 \sqrt{3}}\right| \\ & \quad=\left|\frac{(3 \hat{\mathbf{i}}+4 \hat{\mathbf{k}}) \cdot(\hat{\mathbf{i}}-7 \hat{\mathbf{j}}+5 \hat{\mathbf{k}})}{5 \sqrt{3}}\right| \\ & \quad=\frac{17}{5 \sqrt{3}} \text { units } \end{aligned} $
