Answer
comp$_{\vec{v}}$ $\vec{u}=-24$
Work Step by Step
$\vec{u}=7\vec{i}-24\vec{j}$ $,$ $\vec{v}=\vec{j}$
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:
$\vec{u}\cdot\vec{v}=(7)(0)+(-24)(1)=-24$
Find $|\vec{v}|$:
$|\vec{v}|=\sqrt{0^{2}+1^{2}}=\sqrt{1}=1$
Substitute $\vec{u}\cdot\vec{v}$ into the formula and evaluate:
comp$_{\vec{v}}$ $\vec{u}=\dfrac{-24}{1}=-24$
