Physics - Vectors Question with Solution | TestHub

Let the given vectors be ${\vec{V}}_1=\hat{i}-2\hat{j}+2\hat{k}$ and ${\vec{V}}_2=-2\hat{i}+\hat{j}-\hat{k}$.

The sum of these vectors is ${\vec{V}}_1+{\vec{V}}_2=-\hat{i}-\hat{j}+\hat{k}$.

According to the given condition, $\vec{A}+({\vec{V}}_1+{\vec{V}}_2)=\hat{j}$.

Substituting the sum, we get $\vec{A}+(-\hat{i}-\hat{j}+\hat{k})=\hat{j}$.

$\vec{A}=\hat{j}-(-\hat{i}-\hat{j}+\hat{k})=\hat{i}+2\hat{j}-\hat{k}$.

The magnitude of vector $\vec{A}$ is $|\vec{A}|=\sqrt{1^2+2^2+(-1{)}^2}=\sqrt{6}$.

Answer: $\sqrt{6}$