Write two different vectors having same direction. - Vidyadip

Question

Write two different vectors having same direction.

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Answer

Consider $\vec{P}=\Big(\hat{i}+\hat{j}+\hat{k}\Big)\ \text{and}\ \vec{q}=\Big(2\hat{i}+2\hat{j}+2\hat{k}\Big).$The direction cosines of $\vec{p}$ are given by,
$I=\frac{1}{\sqrt{1^2+1^2+1^2}}=\frac{1}{\sqrt{3}},$ $m=\frac{1}{\sqrt{1^2+1^2+1^2}}=\frac{1}{\sqrt{3}},$ $\text{and}\ n=\frac{1}{\sqrt{1^2+1^2+1^2}}=\frac{1}{\sqrt{3}},$ The direction cosines of $\vec{q}$ are given by,$I=\frac{2}{\sqrt{2^2+2^2+2^2}}=\frac{2}{2\sqrt{3}}=\frac{1}{\sqrt{3}},$ $m=\frac{2}{\sqrt{2^2+2^2+2^2}}=\frac{2}{2\sqrt{3}}=\frac{1}{\sqrt{3}},$ $\text{and}\ n=\frac{2}{\sqrt{2^2+2^2+2^2}}=\frac{2}{2\sqrt{3}}=\frac{1}{\sqrt{3}},$
The direction cosines of $\vec{p}\ \text{and}\ \vec{q}$ are the same. Hence, the tow vectors have the same direction.

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