Math - Quaternion Multiplication (Part 2)

In this lecture we continued our exploration of multiplying two quaternions.

We found that we could reduce our previous polynomial expansion into an easy to read formula and in the process, discovered how both the dot and cross product of two vectors were originally used to help with quaternion multiplication.

We then looked at how to construct a 4x4 matrix for quaternion multiplication.

As a challenge, you were asked to try multiplying the quaternions:
(1 + 2i + 3j + 4k) (5 + 6i + 7j + 8k)

Of the three multiplication options we looked at; which did you use, and which is your favourite?

Hi there
found 0 at cross product, 65 at dot product, finally to obtain
60 + 16i + 22j + 28k

@Caval, great work attempting this challenge.
You are really close to the correct answer, but it looks like you made a mistake when working out the cross product.

Don’t be discouraged though. It’s a big calculation with a lot of moving parts, so it’s easy for minor mistakes to slip in.

Here are the complete calculations so you can double check them against your own:

Somehow I added the component of the cross product together to make zero, weird sub consciou reflex… I had no reason to do that since the output of cross product is a vector. Thanks for the correction

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Don’t worry, it happens to the best of us!
Glad I could help.