Download App

STD 12 - 11. three dimension geometry — Mathematics STD 12 Science — Question

CBSE BoardEnglish MediumSTD 12 ScienceMathematicsSTD 12 - 11. three dimension geometry1 Mark
MCQ
If lines $\frac{{x - 1}}{3} = \frac{{y - 2}}{{ - 1}} = \frac{{z - \lambda }}{2}$ and $\frac{{x + 1}}{{ - 2}} = \frac{y}{{3\lambda }} = \frac{{2z - 7}}{1}$ are coplanar then sum of value $(s)$ of $\lambda $ is
  • ✓
    $\frac{{182}}{{36}}$
  • B
    $\frac{{162}}{{36}}$
  • C
    $\frac{{72}}{{36}}$
  • D
    $\frac{{182}}{2}$
✓

Answer

Correct option: A.
$\frac{{182}}{{36}}$
a
$\left|\begin{array}{ccc}{2} & {2} & {\lambda-\frac{7}{2}} \\ {3} & {-1} & {2} \\ {-2} & {3 \lambda} & {\frac{1}{2}}\end{array}\right|=0$

$\Rightarrow 2\left(-\frac{1}{2}-6 \lambda\right)-2\left(\frac{3}{2}+4\right)+\left(\lambda-\frac{7}{2}\right)(9 \lambda-2)=0$

$\Rightarrow 18 \lambda^{2}-91 \lambda-16=0$

$\Rightarrow \lambda_{1}+\lambda_{2}=\frac{91}{18}=\frac{182}{36}$

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 STD 12 - 11. three dimension geometry→STD 12 - 11. three dimension geometry — all question types→Mathematics STD 12 Science question papers→CBSE Board STD 12 Science question papers→CBSE Board question paper generator→

Similar questions

If $f(x)$ is a polynomial function satisfying the condition $f(x) . f(1/x) = f(x) + f(1/x)$ and $f(2) = 9$ then :
→
If $\left|\begin{array}{ccc}x & \sin \theta & \cos \theta \\ -\sin \theta & -x & 1 \\ \cos \theta & 1 & x\end{array}\right|=8$, then find the value of $x$.
→
The function $f(x) = \frac{{1 - \sin x + \cos x}}{{1 + \sin x + \cos x}}$ is not defined at $x = \pi .$ The value of $f(\pi ),$ so that $f(x)$ is continuous at $x = \pi $, is
→
$\int_{}^{} {\frac{{dx}}{{(x + 1)(x + 2)}} = } $
→
Inverse matrix of $\left[ {\begin{array}{*{20}{c}}4&7\\1&2\end{array}} \right]$
→
Let $\vec a = \hat i + \hat j + \hat k,\,\,\,\vec c = \hat j - \hat k$ and a vector $\vec b$ be such that $\vec a \times \vec b = \,\vec c$ and $\vec a\, \cdot \,\vec b = \,3.$ Then $\left| {\vec b} \right|$ equals?
→
If $\sum_{r=1}^{50} \tan ^{-1} \frac{1}{2 r^{2}}=p$, then the value of $\tan p$ is :
→
The function $f(x) = {x^2}$ is increasing in the interval
→
Let $a, b, c, d$ be in arithmetic progression with common difference $\lambda$. If

$\left|\begin{array}{lll} x+a-c & x+b & x+a \\ x-1 & x+c & x+b \\ x-b+d & x+d & x+c \end{array}\right|=2$

then value of $\lambda^{2}$ is equal to $.....$

→
People living at Mars, instead of the usual definition of derivative $D\,\, f(x)$, define a new kind of derivative, $D^*f(x)$ by the formula

$D^*f(x) =\mathop {Limit}\limits_{h \to 0} \frac{{{f^2}(x + h) - {f^2}(x)}}{h}$ where $f^2(x)$ means $[f(x)]^2.$ If $f(x) = x lnx$ then

${\left. {D^*f(x)} \right|_{x = e}}$ has the value

→