Question

The S.D. between the lines $\overline{r}=(5\hat{i}+7\hat{j}+3\hat{k})+\lambda (5\hat{i}-16\hat{j}+7\hat{k})$
$\overline{r}=(9\hat{i}+13\hat{j}+15\hat{k})+\lambda (3\hat{i}+8\hat{j}-5\hat{k})$ is

• A. $8units$
• B. $12units$
• C. $10units$
• D. None of these

Answer 1

Answer: (D)

None of these

Shortest distance between,

$\Rightarrow \overline{r}=(9i+13j+15k)+\lambda (3i+8j-5k)$

$d=\left|\frac{({\overline{r}}_2-{\overline{r}}_1).(\overline{u}\times \overline{v)}}{|\overline{u}\times \overline{v}|}\right|$

$\overline{u}\times \overline{v}=\left|\begin{array}{ccc}i& j& k\\ 5& -16& 7\\ 3& 8& -5\end{array}\right|$

$=i(80-56)-j(-25-21)+k(40+48)$

$=36i+46j+88k$

$r_2-r_1=4i+6j+12k$

$d=\left|\frac{144+276+1056}{\sqrt{1405}}\right|$

$=\frac{1476}{\sqrt{1405}}$

$=\frac{1476}{37.5}$

$=39.36Units$

Hence the answer is none of these.