Download App

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

CBSE BoardEnglish MediumSTD 12 ScienceMathematicsSTD 12 - 10. vector algebra1 Mark
MCQ
Let $\vec a,\vec b\;$ and $\;\vec c$ be three unit vectors such that  $\vec a \times \left( {\vec b \times \vec c} \right) = \frac{{\sqrt 3 }}{2}\left( {\vec b + \vec c} \right)$ . If  $\vec b$ is not parallel to $\vec c$ then angle between $\vec a\;$ and $\;\vec b$ is :
  • ✓
    $\frac{{5\pi }}{6}$
  • B
    $\frac{{2\pi }}{3}$
  • C
    $\frac{{3\pi }}{4}$
  • D
    $\frac{\pi }{2}$
✓

Answer

Correct option: A.
$\frac{{5\pi }}{6}$
a
$\left(\vec{a} \cdot \vec{c}-\frac{\sqrt{3}}{2}\right) \vec{b}-\left(\vec{a} \cdot \vec{b}+\frac{\sqrt{3}}{2}\right) \vec{c}=0$

$\Rightarrow \vec{a} \cdot \vec{b}=\cos \theta=-\sqrt{3} / 2 $

$\Rightarrow \theta=5 \pi / 6$

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

Area bounded by the curve $y = x^3,$ the $x-$ axis and the ordinates $x = -2$ and $x = 1$ is :
→
If $y = {\tan ^{ - 1}}\left( {{x \over {1 + \sqrt {1 - {x^2}} }}} \right)$, then ${{dy} \over {dx}} = $
→
If the polynomial equation $\text{a}_0\text{x}^{\text{n}}+\text{a}_{\text{n}-1}\text{x}^{\text{n}-1}+\text{a}_{\text{n}-2}\text{x}^{\text{n}-2}+...\text{a}_2\text{x}^2+\text{a}_1\text{x}+\text{a}_0=0$ n positive integer,has two different real roots $\alpha$ and $\beta,$ then between $\alpha$ and $\beta,$ the equation $\text{n}\text{a}_{\text{n}}\text{x}^{\text{n}-1}+(\text{n}-1)\text{a}_{\text{n}-1}\text{x}^{\text{n}-2}+...+\text{a}_1=0$ has:
→
The function $\frac{{\sin \,\,(x\, + \,a)}}{{\sin \,\,(x\, + \,b)}}$ has no maxima or minima if
→
Let $f: R \rightarrow R$ be defined as

$f(x)=\left\{\begin{array}{ll}\frac{x^{3}}{(1-\cos 2 x)^{2}} \log _{e}\left(\frac{1+2 x e^{-2 x}}{\left(1-x e^{-x}\right)^{2}}\right), & x \neq 0 \\ \,\alpha & , x=0\end{array}\right.$ If $\mathrm{f}$ is continuous at $\mathrm{x}=0$, then $\alpha$ is equal to :

→
The total number of distinct $x \in \mathbb{R}$ for which $\left|\begin{array}{ccc}x & x^2 & 1+x^3 \\ 2 x & 4 x^2 & 1+8 x^3 \\ 3 x & 9 x^2 & 1+27 x^3\end{array}\right|=10$ is
→
The area bounded by the $x-$ axis, the curve $y = f(x)$ and the lines $x = 1,\,x = b$ is equal to $\sqrt {{b^2} + 1} - \sqrt 2 $ for all $b > 1$, then $f(x)$ is
→
If the system of equations $\alpha x+y+z=5, x+2 y+$ $3 z=4, x+3 y+5 z=\beta$ has infinitely many solutions, then the ordered pair $(\alpha, \beta)$ is equal to:
→
The function $\text{f(x)}=\begin{cases}\frac{\text{x}^2}{\text{a}},&0\leq\text{x}<1\\\text{a},&1\leq\text{x}<\sqrt{2}\\\frac{2\text{b}^2-4\text{b}}{\text{x}^2},&\sqrt{2}\leq\text{x}<\infty\end{cases}$ is continuous for $0\leq\text{x}<\infty,$ then the most suitable values of $a$ and $b$ are:
→
The derivative of $\cos^{-1}(2\text{x}^2-1)$ with respect to $\cos^{-1}\text{x}$ is :
→