Question

If $a$ and $b$ are two non - zero, non - collinear vectors, then $2[abi]i+2[abj]j+2[abk]k$ is equal to?

• A. $2(a\times b)$
• B. $a\times b$
• C. $a+b$
• D. None of these

Answer 1

The correct option is A

$2(a\times b)$

Explanation for the correct option:

Find the value of vector $2[abi]i+2[abj]j+2[abk]k$:

Let $\overrightarrow{a}=a_1\hat{i}+a_2\hat{j}+a_3\hat{k}$

$\overrightarrow{b}=b_1\hat{i}+b_2\hat{j}+b_3\hat{k}$

$\begin{array}{rcl}\therefore 2[\overrightarrow{a}\overrightarrow{b}\hat{i}]\hat{i}+2[\overrightarrow{a}\overrightarrow{b}\hat{j}]\hat{j}+2[\overrightarrow{a}\overrightarrow{b}\hat{k}]\hat{k}& =& 2\left([\overrightarrow{a}\overrightarrow{b}\hat{i}]\hat{i}+2[\overrightarrow{a}\overrightarrow{b}\hat{j}]\hat{j}+2[\overrightarrow{a}\overrightarrow{b}\hat{k}]\hat{k}\right)\\ & =& 2\left[\left(\left(\overrightarrow{a}\times \overrightarrow{b}\right)\hat{i}\right)\hat{i}+\left(\left(\overrightarrow{a}\times \overrightarrow{b}\right)\hat{j}\right)\hat{j}+\left(\left(\overrightarrow{a}\times \overrightarrow{b}\right)\hat{k}\right)\hat{k}\right]\\ & =& \mathbf{}2(\overrightarrow{\mathrm{a}}\times \overrightarrow{\mathrm{b}})\end{array}$

Hence, Option ‘A’ is Correct.