Question

If a=2i+5j and b=2i-j then the unit vector along a+b will be

√2(i+j) this is answer i don't know how they got this can someone explain ?
plsss

Answer 1

Explanation:

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Answer 2

Given:

a=2i+5j and b=2i-j

To find:

Unit vector along a + b ?

Calculation:

$\vec{a} + \vec{b} = (2 \hat{i} + 5 \hat{j}) + (2\hat{i} - \hat{j})$

$\implies \vec{a} + \vec{b} = (2 + 2) \hat{i} + (5 - 1) \hat{j}$

$\implies \vec{a} + \vec{b} = 4\hat{i} +4 \hat{j}$

Now, the unit vector will be :

• Let the unit vector be c :

$\implies \vec{c} = \dfrac{\vec{a} + \vec{b}}{ | \vec{a} + \vec{b}| }$

$\implies \vec{c} = \dfrac{ 4\hat{i} +4 \hat{j}}{ \sqrt{ {4}^{2} + {4}^{2} } }$

$\implies \vec{c} = \dfrac{ 4(\hat{i} +\hat{j})}{ \sqrt{ 32}}$

$\implies \vec{c} = \dfrac{ 4(\hat{i} +\hat{j})}{ 4\sqrt{2 }}$

$\implies \vec{c} = \dfrac{ \hat{i} +\hat{j}}{ \sqrt{2 }}$

$\implies \vec{c} = \dfrac{ \sqrt{2}( \hat{i} +\hat{j})}{ 2}$

This is the correct answer ✔️