Under construction Stations under construction may not yet contain a good range of resources covering all the key questions and different types of problem.

## How can we define and use products of vectors?

### Key questions

1. 1

What is the scalar product?

2. 2

What is the vector product?

3. 3

How can we describe lines and planes using vectors?

4. 4

What physical quantities arise as scalar or vector products?

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Lines
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Lines
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Resource type Title
Building blocks Is it a plane?

#### Review questions

Title Ref
Can we express a point in this plane in terms of two parameters? R7187
Can we find the angle between the planes $ABC$ and $ABD$? R6449
Can we find the equation of the plane containing $l_1$ and $PQ$? R5089
Can we show the direction of $P'Q'$ is independent of $P$? R8565
Given three vectors, can we find a point equidistant from them all? R5813
If $\overrightarrow{OM}$ is the projection of $\overrightarrow{OA}$ on $m$, where is $M$? R7272
If $a\mathbf{i}+b\mathbf{j}+c\mathbf{k}$ is perpendicular to these vectors, what is $a:b:c$? R6493
What's the position vector of the reflection of $O$ in the plane $ABC$? R9794
Where are $P$ and $Q$ if $PQ$ is perpendicular to $l_1$ and $l_2$? R8828
Where do $ST$ and $AB$ cross? R8456
Which point $P$ is on both this line and this plane? R6006