Answer
comp$_{\vec{v}}$ $\vec{u}=\dfrac{28}{5}$
Work Step by Step
$\vec{u}=7\vec{i}$ $,$ $\vec{v}=8\vec{i}+6\vec{j}$
The component of $\vec{u}$ along $\vec{v}$ is comp$_{\vec{v}}$ $\vec{u}=\dfrac{\vec{u}\cdot\vec{v}}{|\vec{v}|}$
where $\vec{u}\cdot\vec{v}$ is the dot product of the vectors $\vec{u}$ and $\vec{v}$ and $|\vec{v}|$ is the magnitude of the vector $\vec{v}$.
Find $\vec{u}\cdot\vec{v}$ by multiplying corresponding components and adding:
$\vec{u}\cdot\vec{v}=(7)(8)+(0)(6)=56$
Find $|\vec{v}|$:
$|\vec{v}|=\sqrt{8^{2}+6^{2}}=\sqrt{64+36}=\sqrt{100}=10$
Substitute $\vec{u}\cdot\vec{v}$ and $|\vec{v}|$ into the formula and evaluate:
comp$_{\vec{v}}$ $\vec{u}=\dfrac{56}{10}=\dfrac{28}{5}$
