Text: Select all that is true:
Question 18 (4 points)
Consider the 3x3 rotation transformation matrix [Ro] =
tr2 + c tr2 - sr3 tr3 + sr2
t r2r1 + s r3 t r2 + c tr2r3 - s r1 tr3
1 - sr2 t r3r2 + sr1 t r2 + c
tr2 + c tr2r3 - s r1 tr3 - 1 - sr2 t r3r1 + s r2 t r2 + c tr3 + sr1 tr2r3 - sr1 t r2 + c
where c = cos, t = 1 - cos0, and s = sin
Assume that [Ro] = [a a ag] where a1, a2, and az are the images of the unit vectors e, e2, eg under the rotation transformation.
The inverse rotation [Ro]^-1 of [Ro] is equal to
tr2 + c t r21 + s r3 t r3r1 - s r2 t r1 r2 - s r3 t r22 + c tr32 + s r1 trr3 + s r2 tr2r3 - s r1 t r2 + c
The inverse rotation [Ro]^-1 of [Ro] is equal to [Ro]T
and then replacing the angle with -0, and then using cos(-0) = cos(0) = c, 1 - cos(-0) = 1 - cos() = t, and sin(-0) = -sin() = -s
The inverse rotation [Ro]^-1 of [Ro] can be constructed using the opposite axis -r and the same angle e
