Download App

STD 12 - 10. vector algebra — Mathematics STD 12 Science — Question

CBSE BoardEnglish MediumSTD 12 ScienceMathematicsSTD 12 - 10. vector algebra1 Mark
MCQ
The number of distinct real values of $\lambda$, for which the vectors $-\lambda^2 \hat{i}+\hat{j}+\hat{k}, \hat{i}-\lambda^2 \hat{j}+\hat{k}$ and $\hat{i}+\hat{j}-\lambda^2 \hat{k}$ are coplanar, is
  • A
    zero
  • B
    one
  • ✓
    two
  • D
    three
✓

Answer

Correct option: C.
two
c
$\left|\begin{array}{ccc}-\lambda^2 & 1 & 1 \\ 1 & -\lambda^2 & 1 \\ 1 & 1 & -\lambda^2\end{array}\right|$ $=0 \Rightarrow \lambda^6-3 \lambda^2-2=0$

$\Rightarrow\left(1+\lambda^2\right)^2\left(\lambda^2-2\right)=0 \Rightarrow \lambda= \pm \sqrt{2}$.

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

More "M.C.Q (1 Marks)" from STD 12 - 10. vector algebra→STD 12 - 10. vector algebra — all question types→Mathematics STD 12 Science question papers→CBSE Board STD 12 Science question papers→CBSE Board question paper generator→

Similar questions

If $\begin{vmatrix}2\text{x}&5\\8&\text{x}\end{vmatrix}=\begin{vmatrix}6&-2\\7&3\end{vmatrix},$ then x =
→
$\int_0^{\pi / 2} \frac{\sin x-\cos x}{1+\sin x \cos x} d x$ is equal to :
→
If the function $f(x)=x^3+e^{\frac{x}{2}}$ and $g(x)=f^{-1}(x)$, then the value of $g^{\prime}(1)$ is
→
Find the value of x if $\begin{bmatrix}3&\text{3}\\2&\text{x}^2\end{bmatrix}=\begin{bmatrix}5&3\\3&2\end{bmatrix}.$
→
The shortest distance between the lines $\frac{{x - 3}}{2} = \frac{{y + 15}}{{ - 7}} = \frac{{z - 9}}{5}$ and $\frac{{x + 1}}{2} = \frac{{y - 1}}{1} = \frac{{z - 9}}{{ - 3}}$ is
→
Let $\alpha $, $\beta$ $\gamma$, $\delta$ are distinct imaginary roots of

$z^5=1$ then value of $\left| {\begin{array}{*{20}{c}}
  {{e^\alpha }}&{{e^{2\alpha }}}&{{e^{3\alpha  + 1}}}&{ - {e^{ - \delta }}} \\ 
  {{e^\beta }}&{{e^{2\beta }}}&{{e^{3\beta  + 1}}}&{ - {e^{ - \delta }}} \\ 
  {{e^\gamma }}&{{e^{2\gamma }}}&{{e^{3\gamma  + 1}}}&{ - {e^{ - \delta }}} 
\end{array}} \right|$

→
Assume $X,\, Y,\, Z,\, W$ and $P$ are matrices of order $2 \times n,\, 3 \times k,\, 2 \times p, \,n \times 3$ and $p \times k$ respectively. If $n=p,$ then the order of the matrix $7 X-5 Z$ is
→
If the gradient of the tangent at any point $(x, y)$ of a curve which passes through the point $\left( {1,\,\frac{\pi }{4}} \right)$ is $\left\{ {\frac{y}{x} - {{\sin }^2}\left( {\frac{y}{x}} \right)} \right\},$ then equation of the curve is
→
If $\theta $ be the angle between the vectors $a = 2i + 2j - k$ and $b = 6i - 3j + 2k$, then
→
$\int_{ - 1}^1 {|1 - x|dx} = $
→