Let a, b ; and ; c be three unit vectors such that a ( b c ) = 3 … - Vidyadip

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

JEE STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

If $ PN$ is the perpendicular from a point on a rectangular hyperbola $x^2 - y^2 = a^2 $ on any of its asymptotes, then the locus of the mid point of $PN$ is :

If the coefficients of ${x^7}$ and ${x^8}$ in ${\left( {2 + \frac{x}{3}} \right)^n}$ are equal, then $n$ is

If $sin\, \theta = sin\, \alpha$ then $sin\, \frac{\theta }{3}$ =

$\sin 15^\circ + \cos 105^\circ = $

The equation of the locus of the mid points of the chords of the circle $4x^2 + 4y^2 - 12x + 4y + 1 = 0$ that subtend an angle of $\frac{{2\pi }}{3}$ at its centre is

For positive integer $n$, define

$f(n)=n+\frac{16+5 n-3 n^2}{4 n+3 n^2}+\frac{32+n-3 n^2}{8 n+3 n^2}+\frac{48-3 n-3 n^2}{12 n+3 n^2}+\ldots+\frac{25 n-7 n^2}{7 n^2}$

Then, the value of $\lim _{ n \rightarrow \infty} f( n )$ is equal to

The distance of the point $ - \hat i + 2\hat j + 6\hat k$ from the straight line that passes through the point $2\hat i + 3\hat j - 4\hat k$ and is parallel to the vector $6\hat i + 3\hat j - 4\hat k$ is

The number of diagonals in a polygon of $m$ sides is

$\int_0^{2a} {\frac{{f(x)}}{{f(x) + f(2a - x)}}\,dx = } $

Let $\overrightarrow{ a }=\hat{ i }+2 \hat{ j }-\hat{ k }, \overrightarrow{ b }=\hat{ i }-\hat{ j }$ and $\overrightarrow{ c }=\hat{ i }-\hat{ j }-\hat{ k }$ be three given vectors. If $\overrightarrow{ r }$ is a vector such that $\overrightarrow{ r } \times \overrightarrow{ a }=\overrightarrow{ c } \times \overrightarrow{ a }$ and $\overrightarrow{ r } \cdot \overrightarrow{ b }=0,$ then $\overrightarrow{ r } \cdot \overrightarrow{ a } \quad$ is equal to ...........