How much is 3*i*j*k?

unit vectors

1 Answer
Feb 25, 2018

It depends...

Explanation:

If the initial * denotes scalar multiplication and the other two *'s denote vector cross product then the answer is #hat(0)# since:

#3 * hat(i) * hat(j) * hat(k) = 3 * hat(k) * hat(k) = 3 * hat(0) = hat(0)#

On the other hand, if this is all quaternion arithmetic then we find:

#3 * i * j * k = 3k^2 = 3 * -1 = -3#