| , * 20 c 1&1&1 1& ^2 & 1& & ^2 , | = - Vidyadip

MCQ

$\left| {\,\begin{array}{*{20}{c}}1&1&1\\1&{{\omega ^2}}&\omega \\1&\omega &{{\omega ^2}}\end{array}\,} \right| = $

✓
$3\sqrt 3 i$
B
$ - 3\sqrt 3 i$
C
$i\sqrt 3 $
D
$3$

✓

Answer

Correct option: A.

$3\sqrt 3 i$

a
(a) $\left| {\,\begin{array}{*{20}{c}}1&1&1\\1&{{\omega ^2}}&\omega \\1&\omega &{{\omega ^2}}\end{array}\,} \right|\, = 3(\omega - {\omega ^2})$

$ = 3\,\left[ {\frac{{ - 1 + \sqrt 3 i}}{2} - \frac{{ - 1 - \sqrt 3 i}}{2}} \right] = 3\sqrt 3 \,i$.

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

Out of $10$ points in a plane $6$ are in a straight line. The number of triangles formed by joining these points are

If ‘$a$’ and ‘$c$’ are the segments of a focal chord of a parabola and b the semi-latus rectum, then

The vector $z = 3 - 4i$ is turned anticlockwise through an angle of ${180^o}$ and stretched $2.5$ times. The complex number corresponding to the newly obtained vector is

The sum of all positive divisors of $ 960$ is

$\int {\frac{{\cos 2x - 1\,\,}}{{\cos 2x + 1}}dx = } $

If the points with vectors $\alpha \hat{i}+10 \hat{j}+13 \hat{k}$, $6 \hat{i}+11 \hat{j}+11 \hat{k}, \frac{9}{2} \hat{i}+\beta \hat{j}-8 \hat{k}$ are collinear, then $(19 \alpha-6 \beta)^2$ is equal to $...........$.

Two numbers are selected randomly from the set $S = \{ 1,\,2,\,3,\,4,\,5,\,6\} $ without replacement one by one. The probability that minimum of the two numbers is less than $4$ is

If two distinct chords, drawn from the point $(p, q)$ on the circle ${x^2} + {y^2} = px + qy$, (where $pq \ne 0$) are bisected by the $x$ - axis, then

If the lines $ax + 2y + 1 = 0,bx + 3y + 1 = 0$ and $cx + 4y + 1 = 0$ are concurrent, then $a, \,b, \,c$ are in

$\operatorname{cosec} 18^{\circ}$ is a root of the equation :