Angles between vectors (scalar product)

Posted in Maths, Core 4

The scalar product is a method to multiply two vectors together to leave you with a vector. The scalar product between two vectors, a and b is written a.b and is calculated like so for two dimensions:

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And for 3 dimensions:

$Dynamic image 1$

This is used in the equation of the angles between two vectors, a and b:

$Dynamic image 2$

Perpendicular vectors

If the scalar product of two vectors is 0, the vectors are perpendicular to one another.

Example

Example question: Find the angle between vectors a = $Dynamic image 3$ and b = $Dynamic image 4$

Worked solution: First step is to work out |a| and |b| using phythagorus:

$Dynamic image 5$

$Dynamic image 6$

Next, calculate the scalar product of the two vectors:

$Dynamic image 7$

Now plug in the values into the 'angle' equation:

$Dynamic image 8$

A level revision