a [a (a b)] is equal to - Vidyadip

MCQ

$a\times [a\times (a\times b)]$ is equal to

A
$(a \times a\,)\,.\,(b \times a)$
B
$|a \times d{|^2}$
C
$[a\,.\,(a \times b)]\,a$
✓
$(a.\,a)\,(b \times a)$

✓

Answer

Correct option: D.

$(a.\,a)\,(b \times a)$

d
(d) $a \times [a \times (a \times b)] = a \times \{ (a\,.\,b)\,a - (a\,.\,a)b\} $

$ = (a\,.\,b)(a \times a) - (a\,.\,a)(a \times b)$$ = (a\,.\,b)\,0 + (a\,.\,a)(b \times a)$

$ = (a\,.\,a)\,\,(b \times a)$.

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

A bag contains $4$ red and $6$ black balls. A ball is drawn at random from the bag, its colour is observed and this ball along with two additional balls of the same colour are re turned to the bag. Ifnow a ball is drawn at random from the bag, then the probability that this drawn ball is red, is :

Let the function $\mathrm{g}:(-\infty, \infty) \rightarrow\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)$ be given by $g(\mathrm{u})=2 \tan ^{-1}\left(e^{\mathrm{u}}\right)-\frac{\pi}{2}$. Then, $\mathrm{g}$ is

If $f(x) = \left\{ {\begin{array}{*{20}{c}}{{e^{\cos x}}\sin x,}&{|x|\, \le 2}\\{2,}&{{\rm{otherwise}}}\end{array}} \right.$, then $\int_{\, - \,2}^{\,3} {f(x)\,dx} $ is equal to

If $M = \left[ {\begin{array}{*{20}{c}}1&2\\2&3\end{array}} \right]$ and ${M^2} - \lambda M - {I_2} = 0$, then $\lambda = $

If $\vec a = 2\hat i + \hat j + \hat k,\vec b = \hat i + 2\vec j + 2\vec k,\vec c = \vec i + \vec j + 2\hat k$ and $\left( {1 + \alpha } \right)\hat i + \beta \left( {1 + \alpha } \right)\hat j + \gamma \left( {1 + \alpha } \right)\left( {1 + \beta } \right)\hat k = \hat a \times \left( {\vec b \times \vec c} \right)$ , then $\alpha ,\beta ,\gamma $ are

Let $f(x)=\max \{|x+1|,|x+2|, \ldots,|x+5|\}$. Then $\int_{-6}^{0} f(x) d x$ is equal to

The number of arbitrary constants in the particular solution of differential equation of fourth order is:

3
2
1
0

If A and B are two independent events such that P(A) = 0.3 and $\text{P}(\text{A}\cup\text{B})=0.5,$ then P(A|B) - P(B|A) =

$\frac{2}{7}$
$\frac{3}{35}$
$\frac{1}{70}$
$\frac{1}{7}$

If $\text{A}=\begin{vmatrix} 1 &\text{amp; 2} \\ 2 &\text{amp; 1} \end{vmatrix}$ and $\text{f}\text{(x)}=\frac{1+\text{x}}{1-\text{x}},$ then $\text{f}(|\text{A}|)$ is:

$\dfrac{-1}{2}$
$\dfrac{1}{2}$
$\dfrac{-1}{3}$
$\text{None of these}$

If $A=\left[\begin{array}{lll}1 & -1 & 1 \\ 1 & -1 & 1 \\ 1 & -1 & 1\end{array}\right]$, then $A^5-A^4-A^3+A^2$ is equal to