Unit vectors and quaternions This might be a dumb question but recently I came to know about the quaternion number system.
I can't stop wondering, "Are they related to unit vectors in any way? They have similar notations and both seem to be related to Spatial dimensions."

Multiplication of real quaternions can be expressed in terms of multiplication of real numbers and scalar, dot and cross-multiplicaion of real 3-dimensionalvectors; thus for two real quaternions
$$(a+b\mathbf i+c\mathbf j+d\mathbf k)(a'+b'\mathbf i+c'\mathbf j+d'\mathbf k)$$ $$=aa'-(b\mathbf i+c\mathbf j+d\mathbf k)\bullet(b'\mathbf i+c'\mathbf j+d'\mathbf k)$$ $$+a(b'\mathbf i+c'\mathbf j+d'\mathbf k)+a'(b\mathbf i+c\mathbf j+d\mathbf k)$$ $$+(b\mathbf i+c\mathbf j+d\mathbf k) \mathbf x (b'\mathbf i+c'\mathbf j+d'\mathbf k)$$
