Download App

10. vector algebra — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths10. vector algebra1 Mark
MCQ
If $\vec u,\vec v,\vec w $ are non-coplanar vectors and $p,q$ are real numbers,then the equality $[3\vec u \,p\vec v\, p\vec w]^-[p\vec v\, \vec w\, q\vec u]^-[2\vec w\, q\vec v\, q\vec u]=0$ hold for: 
  • A
    exactly two values of  $ (p,q)$
  • B
    more than two but not all values of $ (p,q)$
  • C
    all values of $ (p,q)$
  • ✓
    exactly one value of $ (p,q)$
✓

Answer

Correct option: D.
exactly one value of $ (p,q)$
d
$[3 \bar{u} p \bar{v} p \bar{w}]-[p \bar{v} \bar{w} q \bar{u}]-[2 \bar{w} q \bar{v} q \bar{u}]=0$

$\Rightarrow 3 p^{2}[\bar{u} \bar{v} \bar{w}]-p q[\bar{u} \bar{v} \bar{w}]+2 q^{2}[\bar{u} \bar{v} \bar{w}]=0$

$\Rightarrow\left(3 p^{2}-p q+2 q^{2}\right)[\bar{u} \bar{v} \bar{w}]=0$

$[\bar{u} \bar{v} \bar{w}] \neq 0$

$\therefore 3 p^{2}-p q+2 q^{2}=0$

$\Rightarrow q^{2}-24 q^{2} \geq 0 \Rightarrow-23 q^{2} \geq 0$

$q^{2} \leq 0 \Rightarrow q=0$

And thus $p=0$

Thus $(p, q) \equiv(0,0)$ is only the possibility.

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 10. vector algebra→10. vector algebra — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

The area of the region $\left\{(x, y): y^2 \leq 4 x, x<4, \frac{x y(x-1)(x-2)}{(x-3)(x-4)}>0, x \neq 3\right\}$ is
→
The sum of absolute maximum and absolute minimum values of the function $f(x)=\left|2 x^{2}+3 x-2\right|+\sin x \cos x$ in the interval $[0,1]$ is
→
$A B C D$ is a rhombus, whose diagonals intersect at $E$. Then $\overrightarrow{E A}+\overrightarrow{E B}+\overrightarrow{E C}+\overrightarrow{E D}$ equals
→
Let $y = {x^2}{e^{ - x}}$, then the interval in which $y $ increases with respect to $x$  is
→
The area bounded by the curves $|x| + |y| \geq 1$ and $x^2 + y^2 \geq 1$ is
→
$\int_{}^{} {{{\sin }^3}x\;.\;\cos x\;dx = } $
→
Let a function $f\left( x \right) = \left\{ \begin{gathered}
   - \ln \left( {3x - \left[ {3x} \right]} \right)\,;\,\,3x \ne n;n \in N \hfill \\
  \ln \left( {\operatorname{sgn} \left( {3x} \right)} \right)\,\,\,\,\,\,\,;\,\,3x = n;n \in N \hfill \\ 
\end{gathered}  \right.,$ (where [.] and sgn $(x)$ denotes greatest integer function and signum function respectively) then number of point $(s)$ , where $f(x)$ is minimum in $x  \in  (0, 5)$ , is 
→
Let $g(x)=\int_0^{|x|^{3 / 4}} t^{2 / 3} \sin \frac{1}{t} d t$, for all real $x$. Then, $\lim _{x \rightarrow 0} \frac{g(x)}{x}$ is equal to
→
The value of ' $k$ ' for which the function $f(x)=\left\{\begin{array}{cll}\frac{1-\cos 4 x}{8 x^2}, & \text { if } & x \neq 0 \\ k, & \text { if } & x=0\end{array}\right.$ is continuous at $x=0$ is
→
A die is tossed thrice. A success is getting $1$ or $6$ on a toss. The mean and the variance of number of successes
→