Question

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Answer 1

$\underline{\rm\red{Question - }}$

Given, $\rm \vec A = 2\hat{\imath} - \hat{\jmath}$ and $\rm \vec B = 3\hat{\imath} - 2\hat{\jmath}$

Then find unit vector of $\rm (\vec A + \vec B)$

$\rm \bigcirc \dfrac{5\hat{\imath} + 3\hat{\jmath}}{\sqrt{34}}$

$\rm \bigcirc \dfrac{5\hat{\imath} - 3\hat{\jmath}}{\sqrt{35}}$

$\rm \bigcirc \dfrac{5\hat{\imath} - 3\hat{\jmath}}{\sqrt{34}}$

$\rm \bigcirc \dfrac{5\hat{\imath} + 4\hat{\jmath}}{\sqrt{35}}$

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$\underline{\rm\red{Answer - }}$

The unit vector of $\rm (\vec A + \vec B)$ = $\rm \dfrac{5\hat{\imath} - 3\hat{\jmath}}{\sqrt{34}}$

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$\underline{\rm\red{Solution - }}$

$\underline{\rm\pink{Given - }}$

$\rm \vec A = 2\hat{\imath} - \hat{\jmath}$

$\rm \vec B = 3\hat{\imath} - 2\hat{\jmath}$

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$\underline{\rm\pink{To \: find - }}$

Unit vector of $\rm (\vec A + \vec B)$

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$\underline{\rm\pink{Formula \: used - }}$

$\boxed{\rm\purple{ Unit\: vector = \frac{Vector}{Magnitude\: of \:the \:vector}}}$

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$\rm \vec A = 2\hat{\imath} - \hat{\jmath}$

$\rm \vec B = 3\hat{\imath} - 2\hat{\jmath}$

$\implies$$\rm \vec A + \vec B = ( 3 + 2 )\hat{\imath} + ( - 1 - 2 )\hat{\jmath}$

$\implies$$\rm \vec A + \vec B = 5\hat{\imath} - 3\hat{\jmath}$

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Magnitude of $\rm \vec A + \vec B = |\vec A + \vec B |$

$\implies$$\rm \sqrt{5^2 + (-3)^2}$

$\implies$$\rm \sqrt{25 + 9}$

$\implies$$\rm \sqrt{34}$

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$\rm Unit\: vector = \dfrac{Vector}{Magnitude\: of \:the \:vector}$

$\implies$$\rm \dfrac{5\hat{\imath} - 3\hat{\jmath}}{ \sqrt{34} }$

$\implies$Unit vector of $\rm \vec A + \vec B = \dfrac{5\hat{\imath} - 3\hat{\jmath}}{ \sqrt{34} }$

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