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Vectors

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Vectors

Study Guide

Key Definition

A vector is a quantity that has both magnitude and direction represented as $\overrightarrow{AB}$.

Important Notes

Vectors have both magnitude and direction.
Vectors can represent physical quantities like velocity and force.
Vectors are often written as $\overrightarrow{v}$.
The magnitude of a vector $\overrightarrow{v}$ is written as $|\overrightarrow{v}|$.
Vector addition involves adding components.

Mathematical Notation

$\overrightarrow{AB}$ represents a vector from point A to point B

$|\overrightarrow{v}|$ represents the magnitude of vector $v$

$+$ represents vector addition

Remember to use proper notation when solving problems

Why It Works

Vectors allow us to represent quantities with both magnitude and direction, crucial for accurately describing physical phenomena.

Remember

A vector's magnitude is determined using the Pythagorean theorem: $\sqrt{x^2 + y^2}$.

Quick Reference

Magnitude of a Vector:$|\overrightarrow{v}| = \sqrt{v_x^2 + v_y^2}$

Understanding Vectors

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Video explanation of this concept

Beginner

Start here! Easy to understand

Beginner Explanation

A vector is like an arrow that tells you how far and in what direction to go. It's represented as $\overrightarrow{AB}$.

Practice Problems

Test your understanding with practice problems

Quick Quiz

Single Choice Quiz

Beginner

What is the magnitude of the vector $\overrightarrow{v} = \langle 3, 4 \rangle$?

Real-World Problem

Question Exercise

Intermediate

Teenager Scenario

Imagine you are flying a drone. It moves $10$ units north and $5$ units east. What is the vector describing its movement?

Thinking Challenge

Thinking Exercise

Intermediate

Think About This

A force of $7$ N is applied at an angle of $60^\\circ$ to the horizontal. What are the horizontal and vertical components of the force?

Challenge Quiz

Single Choice Quiz

Advanced

If $\overrightarrow{a} = \langle 1, 2, 3 \rangle$ and $\overrightarrow{b} = \langle 4, 5, 6 \rangle$, what is $\overrightarrow{a} + \overrightarrow{b}$?

Recap

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Review key concepts and takeaways