Question

If $a=1+j+2k$ and $b=3i+j+k$ then the value of $a\times b$ is-

• A. $-i+5j-2k$
• B. $2i+7j+2k$
• C. $3i+7j-2k$
• D. $-i-5j+5k$

Answer 1

The correct option is A $-i+5j-2k$

$a=\hat{i}+\hat{j}+2\hat{k}$ and $b=3\hat{i}+\hat{j}+\hat{k}$

$a\times b=(\hat{i}+\hat{j}+2\hat{k})\times (3\hat{i}+\hat{j}+\hat{k})$

$a\times b=(\hat{i}\times 3\hat{i})+(\hat{i}\times \hat{j})+(\hat{i}\times \hat{k})+(\hat{j}\times 3\hat{i})+(\hat{j}\times \hat{j})+(\hat{j}\times \hat{k})+(2\hat{k}\times 3\hat{i})+(2\hat{k}\times \hat{j})+(2\hat{k}\times \hat{k})$

$a\times b=0+\hat{k}-\hat{j}-3\hat{k}+0+\hat{i}+6\hat{j}-2\hat{i}+0$

$a\times b=\hat{k}-\hat{j}-3\hat{k}+\hat{i}+6\hat{j}-2\hat{i}$

$a\times b=-\hat{i}+5\hat{j}-2\hat{k}$

Hence the correct option is (A).