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If the shortest distance between the line joining the points (1,2,3) and (2,3,4), and the line \frac{x-1}{2}=\frac{y+1}{-1}=\frac{z-2}{0} is a, then 28 \mathrm{a}^2 is equal to

Option: 1

18


Option: 2

-


Option: 3

-


Option: 4

-


Answers (1)

best_answer

A (1, 2, 3)              B (2, 3, 4)

Equation of line AB

\frac{x-1}{1}=\frac{y-2}{1}=\frac{z-3}{1}

Given line

\frac{x-1}{2}=\frac{y+1}{-1}=\frac{z-2}{0}

shortest distance =\left|\frac{\left(\overrightarrow{\mathrm{a}}_2-\overrightarrow{\mathrm{a}}_1\right) \cdot\left(\overrightarrow{\mathrm{b}}_2 \times \overrightarrow{\mathrm{b}}_1\right)}{\left|\overrightarrow{\mathrm{b}}_1 \times \overrightarrow{\mathrm{b}}_2\right|}\right|

\begin{aligned} & =\left|\frac{(3 \hat{\mathrm{j}}-\hat{\mathrm{k}}) \cdot(\hat{\mathrm{i}}+2 \hat{\mathrm{j}}-3 \hat{\mathrm{k}})}{\sqrt{1+4+9}}\right| \\ & \alpha=\frac{3}{\sqrt{14}} \\ & 28 \alpha^2=28 \times \frac{9}{14}=18 \end{aligned}

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