Question

Calculate the unit vector along 2i+3j+5k. Where i,j,k are unit vector along X axis, Y axis and Z axis

respectively​

Answer 1

$\maltese\: \underline{\underline{\sf AnsWer :}}\:\maltese$

Given Parameters;

$\longrightarrow\:\:\sf \overrightarrow{A} = 2\hat{i} + 3\hat{j} + 5\hat{k}$

By using given below formula we can calculate the unit vector :

$\longrightarrow\:\:\sf \hat{A} = \dfrac{ \overrightarrow{A}}{ |\overrightarrow{A}| }$

Now, just substitue the given quantities in above formula :

$\longrightarrow\:\:\sf \hat{A} = \dfrac{2\hat{i} + 3\hat{j} + 5\hat{k}}{ \sqrt{ {(2)}^{2} + {(3)}^{2} + {(5)}^{2} } }$

$\longrightarrow\:\:\sf \hat{A} = \dfrac{2\hat{i} + 3\hat{j} + 5\hat{k}}{ \sqrt{ 4 + 9+ 25} }$

$\longrightarrow\:\: \underline{ \boxed{\bold{ \hat{A} = \dfrac{2\hat{i} + 3\hat{j} + 5\hat{k}}{ \sqrt{38} }} }}$