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Write two different vectors having same direction.
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Verified Answer
Let the two vectors be
$$
\vec{a}=\hat{i}+\hat{j}+\hat{k}, \vec{b}=3 \hat{i}+3 \hat{j}+3 \hat{k}
$$
Direction cosines of $\vec{a}$ are $\left(\frac{1}{\sqrt{3}}, \frac{1}{\sqrt{3}}, \frac{1}{\sqrt{3}}\right)$ and d'c's of $\overrightarrow{\mathrm{b}}$ are $\left(\frac{3}{\sqrt{27}}, \frac{3}{\sqrt{27}}, \frac{3}{\sqrt{27}}\right)$ i.e., $\left(\frac{1}{\sqrt{3}}, \frac{1}{\sqrt{3}}, \frac{1}{\sqrt{3}}\right)$. Hence vectors $\vec{a}$ and $\vec{b}$ have the same direction but different magnitude.
$$
\vec{a}=\hat{i}+\hat{j}+\hat{k}, \vec{b}=3 \hat{i}+3 \hat{j}+3 \hat{k}
$$
Direction cosines of $\vec{a}$ are $\left(\frac{1}{\sqrt{3}}, \frac{1}{\sqrt{3}}, \frac{1}{\sqrt{3}}\right)$ and d'c's of $\overrightarrow{\mathrm{b}}$ are $\left(\frac{3}{\sqrt{27}}, \frac{3}{\sqrt{27}}, \frac{3}{\sqrt{27}}\right)$ i.e., $\left(\frac{1}{\sqrt{3}}, \frac{1}{\sqrt{3}}, \frac{1}{\sqrt{3}}\right)$. Hence vectors $\vec{a}$ and $\vec{b}$ have the same direction but different magnitude.
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