If a = i + j + k, , , b = i - j + k, , , c = i + 2 j + k , then t… - Vidyadip

MCQ

If $\vec a = \hat i + \hat j + \hat k,\,\,\vec b = \hat i - \hat j + \hat k,\,\,\vec c = \hat i + 2\hat j + \hat k$ , then the value of $\left| {\begin{array}{*{20}{c}}
{\vec a.\vec a}&{\vec a.\vec b}&{\vec a.\vec c} \\
{\vec b.\vec a}&{\vec b.\vec b}&{\vec b.\vec c} \\
{\vec c.\vec a}&{\vec c.\vec b}&{\vec c.\vec c}
\end{array}} \right|$ is

A
$2$
B
$4$
✓
$16$
D
$64$

✓

Answer

Correct option: C.

$16$

c
$[\bar{a} \bar{b} \bar{c}]^{2}=\left|\begin{array}{lll}{\bar{a} \cdot \bar{a}} & {\bar{a} \cdot \bar{b}} & {\bar{a} \cdot \bar{c}} \\ {\bar{b} \cdot \bar{a}} & {\bar{b} \cdot \bar{b}} & {\bar{b} \cdot \bar{c}} \\ {\bar{c} \cdot \bar{a}} & {\bar{c} \cdot \bar{b}} & {\bar{c} \cdot \bar{c}}\end{array}\right|$

and $[\bar{a} \bar{b} \bar{c}]=\left|\begin{array}{ccc}{1} & {1} & {1} \\ {1} & {-1} & {1} \\ {1} & {2} & {-1}\end{array}\right|=4$

$\Rightarrow[\bar{a} \bar{b} \bar{c}]^{2}=16$

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

In which of the following intervals is $y=x^2 e^{-x}$ increasing ?

$\mathop {Lim}\limits_{k \to 0} \,\,\frac{1}{k}\int\limits_0^k {{{(1 + \sin 2x)}^{\frac{1}{x}}}dx} $

Choose the correct answer.
Which of the following is correct:

If $\tan^{-1}\Big\{\frac{\sqrt{1+\text{x}^2}-\sqrt{1-\text{x}^2}}{\sqrt{1+\text{x}^2}+\sqrt{1-\text{x}^2}}\Big\}=\alpha,$ then $x^2 =$

The value of the integral $\sum\limits_{k = 1}^n {\int_0^1 {f(k - 1 + x)\,dx} } $ is

If $\displaystyle \begin{vmatrix}\text{x} &\text{amp; } 1 \\ \text{y} &\text{amp; } 2 \end{vmatrix}-\displaystyle \begin{vmatrix}\text{y} &\text{amp; } 1 \\ 8&\text{amp; } 0\end{vmatrix}=\displaystyle \begin{vmatrix}2 &\text{amp; } 0 \\ \text{-x}&\text{amp; } 2\end{vmatrix}$ then the values of $x$ and $y$ respectively are :

If $y = {e^{\sqrt x }}$, then ${{dy} \over {dx}}$ equals

Let $R$ be the relation in the set $N$ given by $R =\{(a,\, b)\,:\, a=b-2,\, b>6\} .$ Choose the correct answer.

Maximize $Z = 11x + 8y,$ subject to $\text{x}\leq4,\text{y}\leq6,\text{x}\geq0,\text{y}\geq0.$

$\int_{}^{} {{e^{{{\tan }^{ - 1}}x}}} \left( {\frac{{1 + x + {x^2}}}{{1 + {x^2}}}} \right)\;dx$ is equal to