## Vectors and three dimensional geometry

**Introduction to vectors and scalars**

**Vector representations example**

**Recognizing vectors**

**Equivalent vectors examples**

**Example finding components of a vector**

**Example comparing x components of vectors**

**Understanding multiplying vectors by scalars**

**Examples from understanding scalar multiplication exercise**

**Example calcuating magnitude of vector from graph**

**Finding vector magnitude from components**

**Vector magnitude from initial and terminal points**

**Adding and subtracting vectors**

**Visually adding and subtracting vectors**

**Subtracting vectors exercise example**

**Adding vectors**

**Combined vector operations example**

**Unit vector intro**

**Intro unit vector notation**

**Scaling unit vector**

**Angles of vectors from components**

**More examples finding vector angles**

**Mag dir vec sums**

**Mag dir vec sums 2**

**Mag vec sums**

**Vector components from magnitude and direction**

**Vector component in direction**

**Adding three vectors**

**Adding displacement vectors**

**Understanding multiplying vectors by scalars**

**Examples from understanding scalar multiplication exercise**

**Vector dot product and vector length**

**Proving vector dot product properties**

**Proof of the cauchy schwarz inequality**

**Linear algebra vector triangle inequality**

**Linear algebra cross product introduction**

**Proof relationship between cross product and sin of angle**

**Dot and cross product comparison intuition**

**Vector triple product expansion very optional**

**Combined vector operations example**

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https://www.khanacademy.org/math

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KHAN ACADEMY® offers great materials that can help build your skills in subjects that are important to you.

You can master basic concepts, explore subjects further or reinforce your knowledge − at your own pace.

KHAN ACADEMY® offers great materials that can help build your skills in subjects that are important to you.

You can master basic concepts, explore subjects further or reinforce your knowledge − at your own pace.

Wherever you are in your learning journey, here are links to free materials that may be useful to identify both your strengths and any knowledge gaps in key background subjects.