Question

Write two differential vectors having same magnitude.

Answer 1

Two vectors can have same magnitude, if the sum of the squares of coefficient of $\hat{i},\hat{j}$ and $\hat{k}$ is same. Let vectors $a=(2\hat{i}+3\hat{j}+\hat{k})$
and $b=(2\hat{i}+3\hat{j}-\hat{k})$ are different vectors having the same magnitude.
Magnitude of Ist vector =$\sqrt{(2{)}^2+(3{)}^2+(1{)}^2}=\sqrt{4+9+1}=\sqrt{14}$
and magnitude of IInd vector =$\sqrt{(2{)}^2+(1{)}^2+(-3{)}^2}=\sqrt{4+1+9}=\sqrt{14}$
i.e., they have same magnitude.