MCQ
$i\,.\,(j \times k) + j\,.\,(k \times i) + k\,.\,(i \times j) = $
  • A
    $1$
  • $3$
  • C
    $-3$
  • D
    $0$

Answer

Correct option: B.
$3$
b
(b) $i\,.\,(j \times k) + j\,.\,(k \times i) + k.(i \times j)$=$i\,.\,i + j\,.\,j + k\,.\,k = 3.$

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

Similar questions

Let $\mathrm{a}, \mathrm{b} \in R, \mathrm{b} \neq 0$, Define a function

$f(x)= \begin{cases}\operatorname{a} \sin \frac{\pi}{2}(x-1), & \text { for } x \leq 0 \\ \frac{\tan 2 x-\sin 2 x}{b x^{3}}, & \text { for } x>0\end{cases}$

If $f$ is continuous at $x=0$, then $10-a b$ is equal to ...... .

Let $A=\{1,3,7,9,11\}$ and $B=\{2,4,5,7,8,10,12\}$. Then the total number of one-one maps $\mathrm{f}: \mathrm{A} \rightarrow \mathrm{B}$, such that $\mathrm{f}(1)+\mathrm{f}(3)=14$, is :
If  $x = \int\limits_{ - y}^y {\frac{{dt}}{{\sqrt {1 + 9{t^2}} }}\,and\,\frac{{{d^2}y}}{{d{x^2}}} = ky} $, then $k$ equals
$\text{I}=\int\frac{(\text{x+a})^3}{\text{x}^3}\text{dx}$ is equal to:
  1. $\text{x}+3\text{a}\log\text{x}-\frac{3\text{a}^2}{\text{x}}-\frac{\text{a}^3}{2\text{x}^2}+\text{c}$
  2. $\text{x}^{2}+3\text{a}\log\text{x}-\frac{3\text{a}^2}{\text{x}}-\frac{\text{a}^3}{2\text{x}^2}+\text{c}$
  3. $\text{x}^{3}+3\text{a}\log\text{x}-\frac{2\text{a}^2}{\text{x}}-\frac{\text{3a}^3}{2\text{x}^2}+\text{c}$
  4. ${1}+2\text{a}\log\text{x}-\frac{2\text{a}^2}{\text{x}}-\frac{\text{3a}^3}{2\text{x}^2}+\text{c}$
Let $A$ be a $2 \times 2$ real matrix and $I$ be the identity matrix of order $2$ . If the roots of the equation $|A-x I|=0$ be $-1$ and $3$ , then the sum of the diagonal elements of the matrix $A^2$ is$..............$
If $m$ and $n$ respectively are the number of local maximum and local minimum points of the function $f ( x )=\int_{0}^{ x ^{2}} \frac{ t ^{2}-5 t +4}{2+ e ^{ t }} dt$, then the ordered pair $( m , n )$ is equal to
In a parallelogram $OACB$ , $\overrightarrow {OA} $ = $\vec a$ , $\overrightarrow {OB} $ = $\vec b$ & foot of perpendicular drawn from point $B$ to $AC$ is $M$ . If $\vec a.\vec b$ = $1$ & $\left| {\vec a} \right| = \left| {\vec b} \right| = 2$ , then $\left| {\overrightarrow {BM} } \right|$ is 
if x lies in the interval [0, 1], then the least value of x2 + x + 1 is :
  1. $3$ 
  2. $\frac{3}{4}$
  3. $1$
  4. none of these.
If a curve passes throught origin, such that length of subnormal is equal to one more than square of ordinate, then
If $\int {\frac{1}{{x + {x^5}}}dx = f(x) + c} $, then the value of $\int {\frac{{{x^4}}}{{x + {x^5}}}dx} $ is