Unit vector r which satisfies r b = r c where b = i + 2 j + k & c… - Vidyadip

MCQ

Unit vector $\vec r$ which satisfies $\vec r \times \vec b = \vec r \times \vec c$ where $\vec b = \hat i + 2\hat j + \hat k$ & $\vec c = 3\hat i + 2\hat k$ , is

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

✓

Answer

Correct option: A.

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

a
$(\vec{r} \times \vec{b})-(\vec{r} \times \vec{c})=\overrightarrow{0} \Rightarrow \vec{r} \times(\vec{b}-\vec{c})=\overrightarrow{0}$

$ \Rightarrow \vec r = \lambda (\vec b - \vec c) = \lambda ( - 2\hat i + 2\hat j - \hat k)$

$ \Rightarrow \hat r = \pm \left( {\frac{{2\hat i - 2\hat j + \hat k}}{3}} \right)$

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

If $a$ and $b$ are chosen randomly from set $\{1,2 ,3,4,5,6\}$ with replacement. Then probability that $\mathop {\lim }\limits_{x \to 0} {\left( {\frac{{{a^x} + {b^x}}}{2}} \right)^{\frac{2}{x}}}=6$ is

A pack of playing cards was found to contain only 51 cards. If the first 13 cards which are examined are all red, then the probability thatthe missing card is black, is:

$\frac13$
$\frac23$
$\frac12$
$\frac{^{25}{\text{C}_{13}}}{^{51}{\text{C}_{13}}}$

Let $v$ be the solution of the differential equation $\left(1-x^{2}\right) d y=\left(xy+\left(x^{3}+2\right) \sqrt{1-x^{2}}\right) d x,-1 < x < 1$ and $y(0)=0$ if $\int\limits_{-\frac{1}{2}}^{\frac{1}{2}} \sqrt{1-x^{2}} y(x) d x=k$ then $k^{-1}$ is equal to:

Choose the correct answer from the given four options.

The domain of the function defined by $\text{f}(\text{x})=\sin^{-1}\sqrt{\text{x}-1}$ is:

[1, 2]
[-1, 1]
[0, 1]
none of these.

The area of ellipse $\frac{\text{x}^2}{4^2}+\frac{\text{y}^2}{9^2}=1$ is:

$6\pi\text{ sq}.\text{units}$
$\frac{\pi(\text{a}^2+\text{b}^2)}{4}\text{ sq}.\text{units}$
$\pi(\text{a+b})\text{ sq}.\text{units}$
$\text{None of these}$

A feasible region of a system of linear inequalities is said to be ______, if it can be enclosed within a circle.

If a line makes angle $\frac{\pi}{3}$ and $\frac{\pi}{4}$ with x-axis and y-axis respectively, then the angle made by the line with z-axis is:

$\frac{\pi}{2}$
$\frac{\pi}{3}$
$\frac{\pi}{4}$
$\frac{5\pi}{12}$

If $f(x) = 2{x^6} + 3{x^4} + 4{x^2}$ then $f'(x)$ is

The distance between the planes given by $r.(i + 2j - 2k) + 5 = 0$ and $r.(i + 2j - 2k) - 8 = 0$ is

Which of the following statements is correct?

Every LPP admits an optimal solution
A LPP admits unique optimal solution
If a LPP admits two optimal solution it has an infinite number of optimal solutions
The set of all feasible solutions of a LPP is not a converse set