Write two different vectors having same magnitude. - Vidyadip

Question

Write two different vectors having same magnitude.

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Answer

Consider $\vec{a}=(\hat{i}-2\hat{j}+3\hat{k})\ \text{and}\ \vec{b}=(2\hat{i}+\hat{j}-3\hat{k}).$ It can be observed that $\Big|\vec{a}\Big|=\sqrt{1^2+(-2)^2+3^2}=\sqrt{1+ 4+9}=\sqrt{14}\ \text{and}$$\Big|\vec{b}\Big|=\sqrt{2^2+1^2+(-3)^2}=\sqrt{4+ 1+9}=\sqrt{14}.$
Hence, $\vec{a}\ \text {and}\ \vec{b}$ are two different vectors having the same magnitude. The vectors are different because they have different directions.

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