If x is a unit vector such that x ( i - 2 j + k ) = - i + k , the… - Vidyadip

MCQ

If $\vec x$ is a unit vector such that $\vec x \times \left( {\hat i - 2\hat j + \hat k} \right) = - \hat i + \hat k$ , then $\vec x$ is

A
$ - \hat i$
✓
$ - \frac{1}{3}\left( {2\hat i - \hat j + 2\hat k} \right)$
C
$ \frac{1}{{\sqrt 3 }}\left( {\hat i - \hat j + \hat k} \right)$
D
$\frac{1}{3}\left( {2\hat i + \hat j + 2\hat k} \right)$

✓

Answer

Correct option: B.

$ - \frac{1}{3}\left( {2\hat i - \hat j + 2\hat k} \right)$

b
Let $\overrightarrow x = a\widehat i + b\widehat j + c\hat k$

$\left|\begin{array}{ccc}{\hat{i}} & {\hat{j}} & {\hat{k}} \\ {a} & {b} & {c} \\ {1} & {-2} & {1}\end{array}\right|=(b+2 c) \hat{i}-\hat{j}(a-c)+\hat{k}(-2 a-b)$

$ = - \widehat i + \widehat k$

$b+2 c=-1, a-c=0$ and $2 a+b=-1$

and $a^{2}+b^{2}+c^{2}=1$

$\Rightarrow a=0, b=-1, c=0$

or $\quad a=-\frac{2}{3}, b=\frac{1}{3}, c=\frac{-2}{3}$

$\Rightarrow \overline{\mathrm{x}}=-\hat{\mathrm{j}}$ or $\quad \overrightarrow{\mathrm{x}}=-\frac{1}{3}(2 \hat{\mathrm{i}}-\hat{\mathrm{j}}+2 \hat{\mathrm{k}})$

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 $f'\left( x \right) = \sin \,\left( {\log \,x} \right)$ and $y = f\,\left( {\frac{{2x + 3}}{{3 - 2x}}} \right)$, then $\frac{{dy}}{{dx}}$ equals

If $x = \sin \left( {2{{\tan }^{ - 1}}2} \right),\,y = \sin \left( {\frac{1}{2}{{\tan }^{ - 1}}\frac{4}{3}} \right),$ then -

Maximize $Z = 10 x_1 + 25 x_2,$ subject to $0\leq\text{x}_{1}\leq3,0\leq\text{x}_{2}\leq3,\text{x}_{1}+\text{x}_{2}\leq5.$

Family of curves whose tangent at a point with its intersection with the curve $xy = c^2$ form an angle of $\frac{\pi }{4}$ is :
where $k$ is an arbitrary constant .

If $\cos x = {1 \over {\sqrt {1 + {t^2}} }}$ and $\sin y = {t \over {\sqrt {1 + {t^2}} }}$, then ${{dy} \over {dx}} = $

Let $\ell_1$ and $\ell_2$ be the lines $\overrightarrow{\mathfrak{1}}_1=\lambda(\hat{\mathrm{i}}+\hat{\mathrm{j}}+\hat{\mathrm{k}})$ and $\vec{r}_2=(\hat{\mathrm{j}}-\hat{\mathrm{k}})+\mu(\hat{\mathrm{i}}+\hat{\mathrm{k}})$, respectively. Let $\mathrm{X}$ be the set of all the planes $\mathrm{H}$ that contain the line $\ell_1$. For a plane $\mathrm{H}$, let $\mathrm{d}(\mathrm{H})$ denote the smallest possible distance between the points of $\ell_2$ and $H$. Let $\mathrm{H}_0$ be plane in $X$ for which $\mathrm{d}\left(\mathrm{H}_0\right)$ is the maximum value of $\mathrm{d}(\mathrm{H})$ as $\mathrm{H}$ varies over all planes in $\mathrm{X}$.

Match each entry in List-$I$ to the correct entries in List-$II$.

List-$I$	List-$II$
($P$) The value of $\mathrm{d}\left(\mathrm{H}_0\right)$ is	($1$) $\sqrt{3}$
($Q$) The distance of the point $(0,1,2)$ from $\mathrm{H}_0$ is	($2$) $\frac{1}{\sqrt{3}}$
($R$) The distance of origin from $\mathrm{H}_0$ is	($3$) $0$
($S$) The distance of origin from the point of intersection of planes $\mathrm{y}=\mathrm{z}, \mathrm{x}=1$ and $\mathrm{H}_0$ is	($4$) $\sqrt{2}$
	($5$) $\frac{1}{\sqrt{2}}$

The corret option is :

The function $f(x) = x^2e^{-x}$ is monotonic increasing when:

If $\left|\begin{array}{lll}\alpha & 3 & 4 \\ 1 & 2 & 1 \\ 1 & 4 & 1\end{array}\right|=0,$ then the value of $\alpha$ is

In each of the following, choose the correct answer:
In a box containing 100 bulbs, 10 are defective. The probability that out of a sample of 5 bulbs, none is defective is

The binary operation $\times$ defined on $N$ by $a \times b = a + b + ab$ for all $a, b \in N$ is: