Question

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

Answer 1

Given:

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

To find:

The unit vector along a+b?

Calculation:

$\vec{a} = 2 \hat{i} + 5 \hat{j}$

$\vec{b} = 2 \hat{i} - \hat{j}$

Now, vector addition:

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

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

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

$\implies \vec{c} =4\hat{i} + 4\hat{j} \: \: \: \: \: ... \: ...(let)$

$\implies \hat{c} = \dfrac{4\hat{i} + 4\hat{j} }{ | \vec{c}| }$

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

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

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

Hope It Helps.