Calculate the new coordinates of a block rotated about x axis by an angle of = 30 degrees. The original coordinates of the block are given relative to the global xyz axis system.
A(1, 1, 2) B(2, I, 2) C(2, 2, 2) D(1, 2, 2) E(1, 1, 1) F(2, 1, 1) G(2, 2,1) 11(1, 2, 1).
just plug the coordinates into your rotation matrix Rx:
1 0 0
0 cosθ -sinθ
0 sinθ cosθ
A' = Rx * AT
and so on
thanks
Can anyone please provide a detailed answer for this question
ndeu495454 43mis1w
To calculate the new coordinates of the block after rotating it about the x-axis by 30 degrees, you can use a rotation matrix.
The rotation matrix for rotating a point (x, y, z) about the x-axis by an angle θ is given by:
| 1 0 0 |
Rx = | 0 cos(θ) -sin(θ) |
| 0 sin(θ) cos(θ) |
First, convert the angle of rotation from degrees to radians. Since the given angle is 30 degrees, the angle in radians is π/6.
Now, let's calculate the new coordinates for each point using the rotation matrix.
For point A(1, 1, 2):
x' = 1
y' = 1 * cos(π/6) - 2 * sin(π/6) = 0.866
z' = 1 * sin(π/6) + 2 * cos(π/6) = 2.732
So, the new coordinates for point A are (1, 0.866, 2.732).
Repeat this process for each of the remaining points, B, C, D, E, F, G, and H, to calculate their new coordinates.