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Q.
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
Vector Algebra
Solution:
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}$