Euler's theorem, states that for any rotation R(t) in 3D where a fixed point is maintained (for example a spinning top with the tip always on the ground) can be described as a simple rotation around an axis. Show this theorem.

Q: (b) A rectangle defined by four points A(0, 0, 0), B(2, 0, 0), C(2, 2, 0) & D(0, 2, 0) is rotated…

A: Given the rectangle with vertices, A(0,0,0), B(2,0,0),C(2,2,0), D(0,2,0). We need to rotate this…

Q: If there is a 60° angle from the positive x-axis to the positive x′-axis, explain how to obtain the…

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Q: What do I do after substituting the expressions for x and y from the rotation formulas into the…

A: The rotation formulas for co-ordinates are if the coordinate is (x,y) then rotate the axis into 90°…

Q: Find the image of the point A(-2, 4, 5) under a rotation of 60 degrees In the plane x = 2 about the…

A: We need to find image of given point.

Q: (i) write down how many lines of symmetry it has (ii) write down the order of rotation symmetry

A: (i) To write the number lines of symmetry the figure has.(ii) To write the order of rotation…

Q: 7. Determine the following for any point P. a) Using the 30° angle as the angle of intersection,…

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Q: Find a parametric representation of a straight line passing through (1,2,1) in the direction of…

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Q: Which of the following describes 2D rotation? OxformMatrix.rotate(0, OxformMatrix.rotate(1,…

A: In two dimensions, the standard rotation matrix has the following form:

Q: 8. 6. A 4 B 2 -8 -6 -4 -2 -2 -4 -6 -8 8, 4, 2.

A:

Q: Triangle ABC is reflected across the y-axis to form the image A’B’C’. Triangle A’B’C’ is then…

A: Triangle ABC is reflected across the y-axis to form the image A'B'C'. Triangle A'B'C' is then…

Q: Find the parametric equations for the line passing through points P(2, -3, 1) and Q(4, 1, -4)

A: Given points are  P2,-3,1,Q4,1,-4