_{Up Learn – A Level maths (edexcel) – 3D Vectors}

_{Up Learn – A Level maths (edexcel) – 3D Vectors}

**Vector Diagrams: Summary**

**Here’s a summary of everything you need to know about vector diagrams**

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### More videos on 3D Vectors:

^{Introduction to 3D Vectors (free trial)}

^{Vectors in 3D (free trial)}

^{3D Column Vector Notation (free trial)}

^{The Third Unit Vector (free trial)}

^{3D Position Vectors (free trial)}

^{3D Vector Arithmetic (free trial)}

^{Paralell Vectors in 3D (free trial)}

^{Perpendicular Vectors in 3D (free trial)}

^{Finding a 3D Vector’s Magnitude (free trial)}

^{Distance Between Points in 3D (free trial)}

## Vectors

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2. What is a vector? – Part 1

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3. What is a vector? – Part 2

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4. Vector Quantities

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5. Vectors and Scalars

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6. Vector arithmetic – Labels – 1

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7. Vector arithmetic – Labels – 2

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8. Vector arithmetic – Labels – 3

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9. Vector Arithmetic – Column Vectors – Part 1

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10. Vector Arithmetic – Column Vectors – Part 2

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11. Vector Arithmetic – Column Vectors – Part 3

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12. Parallel Vectors – Part 1

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13. Parallel Vectors – Part 2

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14. Perpendicular Vectors

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15. Point to Point Notation

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16. The Unit Vectors

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17. Magnitude

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18. Direction

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19. Other Unit Vectors

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20. Position Vectors

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21. Distance Between Points – Part 1

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22. Distance Between Points – Part 2

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23. Using Vectors to Solve Geometric Problems

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2. Vectors in 3D

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3. 3D Column Vector Notation

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4. The Third Unit Vector

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5. 3D Position Vectors

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6. 3D Vector Arithmetic

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7. Paralell Vectors in 3D

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8. Perpendicular Vectors in 3D

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9. Finding a 3D Vector’s Magnitude

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10. Distance Between Points in 3D

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Here’s a reminder of the key points you should know about 3D vectors.

We can use vectors to describe movements in 2D space…

… but also movements in 3D space.

Just like 2D vectors, 3D vectors have a magnitude… and a direction.

And we can give vectors names.

We can represent them using point to point notation… [BA]

… or column vector notation by adding a third value… [(2 5 3) and then pulse the 3]

… or unit vector notation by adding this third unit vector, k. [2i + 5j + 3k and then pulse the 3k.]

To describe the position of a point, we can use coordinates…

Or we can use a position vector instead.

Next, adding 3D vectors works just like adding 2D vectors.

Here’s what it looks like when we add two vectors in column vector notation.

And here’s what it looks like in unit vector form.

Here’s what it looks like when we multiply by a scalar in column vector notation…

… and in unit vector form.

If two vectors are multiples of one another, that means they’re parallel.

Next, we can find the magnitude of a 3D vector using 3D pythagoras.

And to find the distance between two points, we can either use this formula…

Or take the position vector for each point…

… subtract one from the other…

… and then find the magnitude of that new vector.

Finally, if you’re given a vector and asked to find the unit vector that points in the same direction…

Divide the original vector…by its magnitude.

WHAT YOU GET

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**Exclusive Practice Papers**

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**Progress Tracker to A***

Bespoke assessment and practice questions to chart your grade gains as you progress through your A Level Maths revision