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

More "M.C.Q (1 Marks)" from 11. three dimension geometry→11. three dimension geometry — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

If $f\left( x \right) = \left[ x \right] - \left[ {\frac{x}{4}} \right],\,x \in R$ , where $[x]$ denotes the greatest integer function, then

The points with position vectors $60\,i + 3\,j$, $40\,i - 8j,$ $a\,i - 52\,j$ are collinear, if $a = $

$\int\frac{\text{x}^9}{(4\text{x}^2+1)^6}\text{ dx}$ is equal to:

$\frac{1}{5\text{x}}\Big(4+\frac{1}{\text{x}^2}\Big)^{-5}+\text{C}$
$\frac{1}{5}\Big(4+\frac{1}{\text{x}^2}\Big)^{-5}+\text{C}$
$\frac{1}{10\text{x}}\Big(\frac{1}{\text{x}^2}+4\Big)^{-5}+\text{C}$
$\frac{1}{10}\Big(\frac{1}{\text{x}^2}+4\Big)^{-5}+\text{C}$

A unit vector perpendicular to vector $ c $ and coplanar with vectors $a$ and $b$ is

If $A=\left[\begin{array}{ccc}3 & -1 & 2 \\ 2 & 1 & 3 \\ 1 & -3 & K\end{array}\right]$ is non-invertible matrix, then value of K :

If the function $f : R \to R$ is defined by $f(x) = log_a(x + \sqrt {x^2 +1} ), (a > 0, a \neq 1)$, then $f^{-1}(x)$ is

If the value of $x$ satisfying the equation ${\sin ^{ - 1}}\sqrt {1 - {x^2}} = {\tan ^{ - 1}}\sqrt {\frac{2}{x} - 1} $ is $\frac {a}{b}$ (where $a$ and $b$ are coprime), then the value of $a^2 + b^2$ is

Let $y=y(x)$ be the solution of the differential equation $\left(x-x^{3}\right) d y=\left(y+y x^{2}-3 x^{4}\right) d x, x>2$. If $y(3)=3$, then $y(4)$ is equal to :

Let $0 < x < \pi $ and $y(x)$ be given by $(1+\sin x)y^3 - (\cos x)y^2 + 2(1+\sin x)y - 2\cos x$ = $0$ . The derivative of $y$ w .r.t. $\tan \frac {x}{2}$ at $x$ =$\frac {\pi}{2}$ is

Choose the correct answer from the given four options.
The reflection of the point $(\alpha,\beta,\gamma)$ in the xy–plane is: