A unit vector along the vector 4 i-3 k is - Vidyadip

MCQ

A unit vector along the vector $4 \hat{i}-3 \hat{k}$ is

A
$\frac{1}{7}(4 \hat{i}-3 \hat{k})$
B
$\frac{1}{5}(4 \hat{i}-3 \hat{k})$
C
$\frac{1}{\sqrt{7}}(4 \hat{i}-3 \hat{k})$
D
$\frac{1}{\sqrt{5}}(4 \hat{i}-3 \hat{k})$

✓

Answer

$\begin{array}{l}\text {Let } \vec{v}=4 \hat{i}-3 \hat{k} \\ \therefore|\vec{v}|=\sqrt{4^2+(3)^2}=\sqrt{16+9}=\sqrt{25}=5 \\ \text { Now, } \hat{v}=\text { unit vector along } \vec{v} \\ \quad=\frac{\vec{v}}{|\vec{v}|}=\frac{1}{5}(4 \hat{i}-3 \hat{k})\end{array}$

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