Question

The sum of the vectors $a=\hat{i}-2\hat{j}+\hat{k}$, $b=-2\hat{i}+4\hat{j}+5\hat{k}$ and $c=\hat{i}-6\hat{j}-7\hat{k}$ is

• A. $-3\hat{j}+\hat{k}$
• B. $-4\hat{j}+\hat{k}$
• C. $-4\hat{j}-\hat{k}$
• D. None of these

Answer 1

Answer: (C)

To find the sum of different vectors, components ( $\hat{i},\hat{j}$ and $\hat{k}$ ) are added separately.
Here, given $a=\hat{i}-2\hat{j}+\hat{k},b=-2\hat{i}+4\hat{j}+5\hat{k},c=\hat{i}-6\hat{j}-7\hat{k}$ Sum of these vectors can be calculated by adding their $\hat{i},\hat{j}$ and $\hat{k}$ components.
$\therefore a+b+c=(\hat{i}-2\hat{j}+\hat{k})+(-2\hat{i}+4\hat{j}+5\hat{k})+(\hat{i}-6\hat{j}-7\hat{k})$
$=(\hat{i}-2\hat{i}+\hat{i})+(-2\hat{j}+4\hat{j}-6\hat{j})+(\hat{k}+5\hat{k}-7\hat{k})$
$=0\hat{i}-4\hat{j}-\hat{k}=-4\hat{j}-\hat{k}$