Applying the Formula
Lets see how close my guess is:
- The two vectors are represented by:
- f = (2, 4, 6)T
- g = (6, 4, 3)T
- The lengths are:
- | f |2 = (2, 4, 6)T · (2, 4, 6)T = 4 + 16 + 36 = 56
- | g |2 = (6, 4, 3)T · (6, 4, 3)T = 36 + 16 + 9 = 61
- The normalized vectors are:
- fu =
(2, 4, 6)T / √56
- gu =
(6, 4, 3)T / √61
- The dot product is:
- fu · gu =
(2, 4, 6)T · (6, 4, 3)T / ( √56 √61)
- = (12+16+18)/( √56 √61)
= 46 / ( √56 √61)
= 0.78704
- The angle is:
- cos θ = 0.78704
- θ = arc cos 0.78704
= 38.1°
Not too far off from my guess.