Answer
comp$_{\vec{v}}$ $\vec{u}=\dfrac{-12}{5}$
Work Step by Step
$\vec{u}=\langle4,6\rangle$ $,$ $\vec{v}=\langle3,-4\rangle$
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:
$\vec{u}\cdot\vec{v}=(4)(3)+(6)(-4)=12-24=-12$
Find $|\vec{v}|$:
$|\vec{v}|=\sqrt{3^{2}+(-4)^{2}}=\sqrt{9+16}=\sqrt{25}=5$
Substitute $\vec{u}\cdot\vec{v}$ and $|\vec{v}|$ into the formula and evaluate:
comp$_{\vec{v}}$ $\vec{u}=\dfrac{-12}{5}$
