Question

Write down the rotation matrix for rotating 30° about the axis (1, 1, 1)

Answer 1

The rotation matrix for rotating 30° about the axis (1, 1, 1) is R = I + (1/2)(K) + (1 - sqrt(3)/2)(K^2).

Step-by-step explanation:

To write down the rotation matrix for rotating 30° about the axis (1, 1, 1), we can use the Rodrigues' rotation formula. The formula is given by:

R = I + sin(theta)(K) + (1 - cos(theta))(K^2)

where R is the rotation matrix, I is the identity matrix, theta is the angle of rotation in radians, and K is the skew-symmetric matrix formed by the axis of rotation.

In this case, the angle of rotation is 30° (converted to radians, it is pi/6) and the axis of rotation is (1, 1, 1). So, we can substitute these values into the formula to calculate the rotation matrix:

R = I + sin(pi/6)(K) + (1 - cos(pi/6))(K^2)

Calculating the values of sin(pi/6) and cos(pi/6), we get:

R = I + (1/2)(K) + (1 - sqrt(3)/2)(K^2)

So, the rotation matrix for rotating 30° about the axis (1, 1, 1) is:

R = I + (1/2)(K) + (1 - sqrt(3)/2)(K^2)