3d Rotational Transforms.docx

3D Rotational Transforms

1. A point P (2, 3, 4) is attached to a rotating frame. The frame rotates 90 degrees about the xaxis of the reference frame. Find the coordinates of the point relative to the reference frame after the rotation. 2. Find the coordinates of point P (2 3 4) relative to the reference frame after a rotation of 45 degrees about the x-axis. 3. Find the coordinates of point P (3 5 7) relative to the reference frame after a rotation of 30 degrees about the z-axis. 4. The point P with coordinates (0 1 1) is rotated about the reference y-axis by π/2. Find the coordinates of the point with respect to reference frame. 5. The coordinates of a point Pa with respect to the reference frame Fa is given by (1, 1, 0). A new frame Fb is generated by rotating the frame Fa by 90 degrees about the Za-axis. Find the new coordinates of the point Pa with respect to the frame Fb. 6. The coordinates of a point Pa with respect to the reference frame Fa is given by (1, 1, 0). A new frame Fc is generated by rotating the frame Fa by -90 degrees about the Yb-axis. Find the new coordinates of the point Pa with respect to the frame Fc.