Hi Everyone, Post your solutions to the Feb 20 In-Class Exercise to this thread. Best, Chris

-- Feb 20 In-Class Exercise Thread

Hi everybody, @BT@||((1),(2),(3),(4))|| = sqrt(1^2 + 2^2 + 3^2 + 4^2) = sqrt(30)@BT@ @BT@||((-2),(1),(2),(1))|| = sqrt((-2)^2 + 1^2 + 2^2 + 1^2) = sqrt(10)@BT@ @BT@q1 \cdot q2 = ((-14), (-8), (-2), (-6))@BT@ @BT@((cos(\pi/4)), (sin(\pi/4) 1/sqrt(3) ((1), (1), (1)))) \approx ((0.71), (0.41), (0.41), (0.41))@BT@

-- Feb 20 In-Class Exercise Thread

I got √30 for the length of the first vector and √10 for the second. Their quaternionic product is (-14, -8, -2, -6).

-- Feb 20 In-Class Exercise Thread

consider the 2 quaternions: [1 2 3 4]^t [-2 1 2 1]^t length of [1 2 3 4]^t is sqroot(30) length of [-2 1 2 1]^t is sqroot(10) multiplication of [1 2 3 4]^t [-2 1 2 1]^t is [-14 -8 -2 -6]^t rotation by pi/2 abt (1,1,1) vector is [cos(pi/4) (sqroot(3)^-1)*sin(pi/4)*[1 1 1]^t]^t

-- Feb 20 In-Class Exercise Thread

	 ||(1,2,3,4)||= sqrt(30)
         ||(-2,1,2,1)||= sqrt(10)

         Quaternionic product: (-14, -8, -2, -6)

         ((cos(pi/4)), ( (1/sqrt(3) *sin(pi/4))*(1,1,1))) 
         = ((1/sqrt(2), ((1/sqrt(2))*  (1/sqrt(3))* (1,1,1)))

1/ ||(1,2,3,4)||= sqrt(30) ||(-2,1,2,1)||= sqrt(10) 2/ Quaternionic product: (-14, -8, -2, -6) 3/ ((cos(pi/4)), ( (1/sqrt(3) *sin(pi/4))*(1,1,1))) = ((1/sqrt(2), ((1/sqrt(2))* (1/sqrt(3))* (1,1,1)))

-- Feb 20 In-Class Exercise Thread

   Length of matrix 2 (m2) = 3.162

1. Length of matrix 1 (m1) = 5.477 Length of matrix 2 (m2) = 3.162 2. m1*m2 = [-14 -8 -2 -6]^t <br> 3. Rotation of (1 1 1) by pi/2 = [0.707 0.577 0.577 0.577]^t

-- Feb 20 In-Class Exercise Thread

(length of quaternion [1, 2, 3, 4]) = sqrt(30) (length of quaternion [-2, 1, 2, 1]) = sqrt(10) product = [-14, -8, -2, -6] rotation by pi/2 about (1, 1, 1): [sqrt(2)/2, (sqrt(2)/2) * ((sqrt(3)/3) * (1, 1, 1))]

-- Feb 20 In-Class Exercise Thread

1. sqrt(30), sqrt(10) 2. [-14, -8, -2, -6] 3. [cos(pi/4), sin(pi/4)/sqrt(3), sin(pi/4)/sqrt(3), sin(pi/4)/sqrt(3)]