Question
Find a unit vector parallel to the vector $3\hat{\text{i}}+7\hat{\text{j}}+4\hat{\text{k}}.$
✓
Answer
Let $3\hat{\text{i}}+7\hat{\text{j}}+4\hat{\text{k}}=\vec{\text{a}}.$
$|\vec{\text{a}}|=\sqrt{3^2+7^2+4^2}$
$=\sqrt{9+49+16}=\sqrt{74}$
Using vector in the direction of
$\vec{\text{a}}=\frac{\vec{\text{a}}}{|\vec{\text{a}}|}=\frac{3\hat{\text{i}}+7\hat{\text{j}}+4\hat{\text{k}}}{\sqrt{74}}$
$|\vec{\text{a}}|=\sqrt{3^2+7^2+4^2}$
$=\sqrt{9+49+16}=\sqrt{74}$
Using vector in the direction of
$\vec{\text{a}}=\frac{\vec{\text{a}}}{|\vec{\text{a}}|}=\frac{3\hat{\text{i}}+7\hat{\text{j}}+4\hat{\text{k}}}{\sqrt{74}}$
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