The constant value ( + ) for which the lines r = 2i + j + k + (i … - Vidyadip

MCQ

The constant value ($\lambda$ + $\mu$) for which the lines $\vec{r}$ = $2\hat{i}$ + $\hat{j}$ + $\hat{k}$ + $\lambda$($\hat{i} - 2\hat{j}$) and $\vec{r}$ = $\hat{i}$ + $\hat{j}$ - $3\hat{k}$ + $\mu$ ($\hat{j} + 2\hat{k}$) intersect each other, is equal to (where $\lambda$ & $\mu$ are parameters)

A
$2$
B
$-1$
C
$0$
✓
$1$

✓

Answer

Correct option: D.

$1$

d
If lines $\vec r = (2 + \lambda )\widehat {\rm{i}} + (1 - 2\lambda )\widehat {\rm{j}} + \widehat {\rm{k}}$

and $\overrightarrow r = \widehat i + (1 + \mu )\widehat j + ( - 3 + 2\mu )\widehat k$

intersects each other, then

$2+\lambda=1,1-2 \lambda=1+\mu $ and $ 1=-3+2 \mu$

$\Rightarrow \lambda=-1, \mu=2$

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 $\mathrm{A}=\left[\mathrm{a}_{\mathrm{ij}}\right]$ and $\mathrm{B}=\left[\mathrm{b}_{\mathrm{ij}}\right]$ be two $3 \times 3$ real matrices such that $b_{i j}=(3)^{(i+j-2)} a_{j i},$ where $\mathrm{i}, \mathrm{j}=1,2,3 .$ If the determinant of $\mathrm{B}$ is $81,$ then the determinant of $A$ is

$\mathop \smallint \limits_{ - \pi /2}^{\pi /2} \frac{{{{\sin }^2}x}}{{1 + {2^x}}}dx =$ . .. .

The lateral edge of a regular rectangular pyramid is $'a'$ cm long . The lateral edge makes an angle $\alpha$ with the plane of the base. The value of $\alpha$ for which the volume of the pyramid is greatest, is

If $2 \times {}^n{C_5} = 9\,\, \times \,\,{}^{n - 2}{C_5}$, then the value of $n$ will be

The standard deviation of $25$ numbers is $40$. If each of the numbers is increased by $5$, then the new standard deviation will be

$\int_{}^{} {\sqrt {\frac{x}{{{a^3} - {x^3}}}} \;dx = } $

The value of $\int \limits_{0}^{\pi} \frac{e^{\cos x} \sin x}{\left(1+\cos ^{2} x\right)\left(e^{\cos x}+e^{-\cos x}\right)} d x$ is equal to

A class has $175$ students. The following data shows the number of students obtaining one or more subjects. Mathematics $100$, Physics $70$, Chemistry $40$; Mathematics and Physics $30$, Mathematics and Chemistry $28$, Physics and Chemistry $23$; Mathematics, Physics and Chemistry $18$. How many students have offered Mathematics alone

If the line $y - \sqrt 3 x + 3 = 0$ cuts the parabola $y^2 = -x -2$ at $A$ and $B, $ then $PA \cdot PB$ is equal to where $P \equiv ( \sqrt 3 , 0)$

A dice is thrown ten times. If getting even number is considered as a success, then the probability of four successes is