| . . .
| We can write
| A = ||A|| a'
| where a' is a unit vector in the direction of A.
|
| We can write some other vector B as
| B = ||B|| (a' cos(theta) + a" sin(theta))
| where a" is some unit vector perpendicular to A.
| Then just take these expressions for A and B, plug
| them into the definition of ||A /\ B|| and turn the
| crank. The result follows immediately:
| ||A /\ B|| = ||A|| ||B|| |sin(theta)|
| . . .From: "John S. Denker" <jsd@MONMOUTH.COM>
Help me here, John. I'm getting a negative value for the square of the
norm of A /\ B:
||A /\ B||^2 = . . .
= ( ||A|| ||B|| Sin(th) )^2 (a' /\ a")(a" /\ a')
But the geometric product (a' /\ a")(a" /\ a') equals -1 . (No?)
Can you devine my errors? If needed I'll fill in more details of my
procedure.