Mathematics - Vector Question with Solution | TestHub

Let the values of p , for which the shortest distance between the lines $\frac{x+1}{3}=\frac{y}{4}=\frac{z}{5}$ and $\overrightarrow{\mathrm{r}}=(\mathrm{p}\hat{\mathrm{i}}+2\hat{\mathrm{j}}+\hat{\mathrm{k}})+\lambda (2\hat{\mathrm{i}}+3\hat{\mathrm{j}}+4\hat{\mathrm{k}})$ is $\frac{1}{\sqrt{6}}$, be $\mathrm{a},\mathrm{b}$, $(a<b)$. Then the length of the latus rectum of the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ is :-