Answer
Horizontal component $=-\dfrac{\sqrt{2}}{2}$
Vertical component $=-\dfrac{\sqrt{2}}{2}$
$\vec{v}=-\dfrac{\sqrt{2}}{2}\vec{i}-\dfrac{\sqrt{2}}{2}\vec{j}$
Work Step by Step
$|\vec{v}|=1$ $;$ $\theta=225^{\circ}$
Multiply the magnitude of the vector $\vec{v}$ by the cosine of $\theta$ to obtain its horizontal component:
Horizontal component
$|\vec{v}|\cos\theta=1\cos225^{\circ}=(1)\Big(-\dfrac{\sqrt{2}}{2}\Big)=-\dfrac{\sqrt{2}}{2}$
Multiply the magnitude of the vector $\vec{v}$ by the sine of $\theta$ to obtain its vertical component:
Vertical component
$|\vec{v}|\sin\theta=1\sin225^{\circ}=(1)\Big(-\dfrac{\sqrt{2}}{2}\Big)=-\dfrac{\sqrt{2}}{2}$
Write the vector in terms of $\vec{i}$ and $\vec{j}$. Do so by adding the product between its horizontal component and $\vec{i}$ and the product between its vertical component and $\vec{j}$:
$\vec{v}=-\dfrac{\sqrt{2}}{2}\vec{i}-\dfrac{\sqrt{2}}{2}\vec{j}$
