Question

Find unit vector of 4i-3j+k

Answer 1

Answer:

Simple Just see the explanation ;

Explanation:

Unit Vector =

$\frac{a \: vector}{ |a| }$

$|a| = \sqrt{ {a}^{2} + {b}^{2} + {c}^{2} }$

Unit Vector = 4i-3j-k / √26

Answer 2

Unit vector of 4i - 3j + k

Let the vector be :

$\vec{r} = 4 \hat{i} - 3 \hat{j} + k$

Now, the general expression for unit vector will be:

$\hat{r} = \dfrac{ \vec{r}}{ | \vec{r}| }$

$\implies \hat{r} = \dfrac{ 4 \hat{i} - 3 \hat{j} + \hat{k}}{ \sqrt{ {4}^{2} + {( - 3)}^{2} + {1}^{2} } }$

$\implies \hat{r} = \dfrac{ 4 \hat{i} - 3 \hat{j} + \hat{k}}{ \sqrt{16 + 9 + 1 } }$

$\implies \hat{r} = \dfrac{ 4 \hat{i} - 3 \hat{j} + \hat{k}}{ \sqrt{26} }$

So, final answer is :

The unit vector is $\dfrac{ 4 \hat{i} - 3 \hat{j} + \hat{k}}{ \sqrt{26} }$