Find a unit vector in the direction of the vector 3 i+4 j. - Vidyadip

Question

Find a unit vector in the direction of the vector $3 \hat{i}+4 \hat{j}$.

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Answer

Given: $\quad \overrightarrow{ v }=3 \hat{ i }+4 \hat{ j }$
$\therefore \quad$ Magnitude of $\overrightarrow{ V }=|\overrightarrow{ V }|=\sqrt{3^2+4^2}=\sqrt{25}=5$
Let $\vec{V}=\hat{\alpha}|\overrightarrow{ V }|$, where $\hat{\alpha}$ is a unit vector
along $\overrightarrow{ V }$
$\therefore \quad \hat{\alpha}=\frac{\overrightarrow{ V }}{|\overrightarrow{ V }|}=\frac{3 \hat{ i }+4 \hat{ j }}{5}=\frac{3}{5} \hat{ i }+\frac{4}{5} \hat{ j }$
Required unit vector is $\frac{ 3 }{5} \hat{ i }+\frac{ 4 }{5} \hat{ j }$.

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