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


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:


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


{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}

Learn more about this topic:

Vectors: Definition, Types & Examples

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

Chapter 57 / Lesson 3

Related to this Question

Explore our homework questions and answers library