Let A ( + 2, 1 - 2 , + 2) and B (2k + 1, k, k +1) and , k R. Then… - Vidyadip

MCQ

Let $A \equiv (\lambda + 2, 1 - 2\lambda , \lambda + 2)$ and $B \equiv (2k + 1, k, k +1)$ and $ \lambda , k \in R.$ Then minimum distance between $A$ and $B$ is -

A
$0$
B
$\frac{1}{{\sqrt {35} }}$
C
$\frac{{\sqrt 3 }}{{\sqrt {35} }}$
✓
$\frac{3}{{\sqrt {35} }}$

✓

Answer

Correct option: D.

$\frac{3}{{\sqrt {35} }}$

d
$\overrightarrow{\mathrm{r}}=(-2,-1,-2)+\lambda(1,-2,1)$

$\overrightarrow{\mathrm{r}}=(-1,0,-1)+\mathrm{k}(2,1,1)$

${\rm{S}}.{\rm{D}} = \left| {\frac{{(\hat i + \hat j + \hat k) \cdot (\hat i - 2\hat j + \hat k) \times (2\hat i + \hat j + \hat k)}}{{|(\hat i - 2\hat j + \hat k) \times (2\hat i + \hat j + \hat k)|}}} \right| = \frac{3}{{\sqrt {35} }}$

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