# Let \vec{u}= 8i - 6j and \vec{v}= -5i + 8j. Find the vector u + v.

## Question:

Let {eq}\vec{u}= 8i - 6j {/eq} and {eq}\vec{v}= -5i + 8j {/eq}. Find the vector u + v.

## Addition of Vectors:

The addition between two vectors can be done through the addition of its components. If the system is two-dimensional then each vector will have two components, one horizontal denoted as: x, and another vertical denoted as: y. The result of this mathematical operation will be another vector.

## Answer and Explanation:

**Data: **

{eq}\vec{u}=\left \langle 8, -6 \right \rangle \\ \vec{v}=\left \langle -5, 8 \right \rangle {/eq}

**Calculations: **

{eq}\begin{align*} \vec{w}&=\vec{u}+\vec{v} \\ \vec{w}&=\left \langle 8, -6 \right \rangle +\left \langle -5, 8 \right \rangle \\ \vec{w}&=\left \langle 8-5, -6+8 \right \rangle \\ \vec{w}&=\left \langle 3, 2 \right \rangle \end{align*} {/eq}

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from Common Entrance Test (CET): Study Guide & Syllabus

Chapter 57 / Lesson 3