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

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

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

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

JEE STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

Let $x=x(y)$ be the solution of the differential equation $2 y \,e^{x / y^{2}} d x+\left(y^{2}-4 x e^{x / y^{2}}\right) d y=0$ such that $x(1)=0$. Then, $x(e)$ is equal to

Let $[x]$ denotes the greatest integer less than or equal to $x$. If $f(x) = [x\sin \pi x]$, then $f(x)$ is

The solution of $\frac{{dy}}{{dx}} = \sin (x + y) + \cos (x + y)$ is

Let $\vec{a}$ and $\vec{b}$ be two unit vectors such that the angle between them is $\frac{\pi}{3}$. If $\lambda \vec{a}+2 \vec{b}$ and $3 \vec{a}-\lambda \vec{b}$ are perpendicular to each other, then the number of values of $\lambda$ in $[-1,3]$ is :

Let $\mathrm{f}$ be any continuous function on $[0,2]$ and twice differentiable on $(0,2)$. If $\mathrm{f}(0)=0, \mathrm{f}(1)=1$ and $f(2)=2$, then

If ${a_1},{a_2},{a_3}.....{a_n}....$ are in $G.P.$ then the value of the determinant $\left| {\,\begin{array}{*{20}{c}}{\log {a_n}}&{\log {a_{n + 1}}}&{\log {a_{n + 2}}}\\{\log {a_{n + 3}}}&{\log {a_{n + 4}}}&{\log {a_{n + 5}}}\\{\log {a_{n + 6}}}&{\log {a_{n + 7}}}&{\log {a_{n + 8}}}\end{array}\,} \right|$ is

Let $R = \{(1, 3), (4, 2), (2, 4), (2, 3), (3, 1)\}$ be a relation on the set $A = \{1, 2, 3, 4\}$. The relation $R$ is

Consider a function $f:R \to R$

$f\left( {x + a} \right) = \frac{1}{2} + \sqrt {f\left( x \right) - {f^2}\left( x \right)}$ a is a real constant, then $f(x)$ must be

Let $A = \{1, 2, 3, 4\}$ and let $R= \{(2, 2), (3, 3), (4, 4), (1, 2)\}$ be a relation on $A$. Then $R$ is

The ${20^{th}}$ term of the series $2 \times 4 + 4 \times 6 + 6 \times 8 + .......$ will be