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The coordinates of point P in frame {1} are [3.0 2.0 1.0]T. The position vector P is rotated about the x-axis by 60° in CCW direction. The sum of the coordinates of point Q (the new position of point P) will be . (Correct up to three decimal place)
Correct answer is '5.367'. Can you explain this answer?
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The coordinates of point P in frame {1} are [3.0 2.0 1.0]T. The positi...
Frame (2) is rotated relative to frame (1) about x-axis by 60o
Sum of coordinates of point Q = 3.00 + .0134 + 2.232 = 5.366
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The coordinates of point P in frame {1} are [3.0 2.0 1.0]T. The positi...
To rotate a point in three-dimensional space about the x-axis, we can use a rotation matrix.
The rotation matrix for a rotation about the x-axis by an angle θ is given by:
R_x = [1 0 0
0 cos(θ) -sin(θ)
0 sin(θ) cos(θ)]
In this case, the angle of rotation is 60 degrees, which is equivalent to π/3 radians. So, we can substitute θ = π/3 into the rotation matrix.
R_x = [1 0 0
0 cos(π/3) -sin(π/3)
0 sin(π/3) cos(π/3)]
Evaluating the trigonometric functions, we get:
R_x = [1 0 0
0 0.5 -√3/2
0 √3/2 0.5]
To rotate a point P = [3.0 2.0 1.0]ᵀ about the x-axis by 60 degrees, we can multiply the rotation matrix R_x with the position vector P.
P_rotated = R_x * P
Calculating the matrix multiplication, we get:
P_rotated = [1 0 0 [3.0
0 0.5 -√3/2 * 2.0
0 √3/2 0.5] 1.0]
P_rotated = [3.0
-√3 + 1
√3/2 + 1]
Therefore, the coordinates of point P after rotating about the x-axis by 60 degrees are [3.0, -√3 + 1, √3/2 + 1].
The rotation matrix for a rotation about the x-axis by an angle θ is given by:
R_x = [1 0 0
0 cos(θ) -sin(θ)
0 sin(θ) cos(θ)]
In this case, the angle of rotation is 60 degrees, which is equivalent to π/3 radians. So, we can substitute θ = π/3 into the rotation matrix.
R_x = [1 0 0
0 cos(π/3) -sin(π/3)
0 sin(π/3) cos(π/3)]
Evaluating the trigonometric functions, we get:
R_x = [1 0 0
0 0.5 -√3/2
0 √3/2 0.5]
To rotate a point P = [3.0 2.0 1.0]ᵀ about the x-axis by 60 degrees, we can multiply the rotation matrix R_x with the position vector P.
P_rotated = R_x * P
Calculating the matrix multiplication, we get:
P_rotated = [1 0 0 [3.0
0 0.5 -√3/2 * 2.0
0 √3/2 0.5] 1.0]
P_rotated = [3.0
-√3 + 1
√3/2 + 1]
Therefore, the coordinates of point P after rotating about the x-axis by 60 degrees are [3.0, -√3 + 1, √3/2 + 1].
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The coordinates of point P in frame {1} are [3.0 2.0 1.0]T. The position vector P is rotated about the x-axis by 60° in CCW direction. The sum of the coordinates of point Q (the new position of point P) will be . (Correct up to three decimal place)Correct answer is '5.367'. Can you explain this answer?
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The coordinates of point P in frame {1} are [3.0 2.0 1.0]T. The position vector P is rotated about the x-axis by 60° in CCW direction. The sum of the coordinates of point Q (the new position of point P) will be . (Correct up to three decimal place)Correct answer is '5.367'. Can you explain this answer? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about The coordinates of point P in frame {1} are [3.0 2.0 1.0]T. The position vector P is rotated about the x-axis by 60° in CCW direction. The sum of the coordinates of point Q (the new position of point P) will be . (Correct up to three decimal place)Correct answer is '5.367'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The coordinates of point P in frame {1} are [3.0 2.0 1.0]T. The position vector P is rotated about the x-axis by 60° in CCW direction. The sum of the coordinates of point Q (the new position of point P) will be . (Correct up to three decimal place)Correct answer is '5.367'. Can you explain this answer?.
The coordinates of point P in frame {1} are [3.0 2.0 1.0]T. The position vector P is rotated about the x-axis by 60° in CCW direction. The sum of the coordinates of point Q (the new position of point P) will be . (Correct up to three decimal place)Correct answer is '5.367'. Can you explain this answer? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about The coordinates of point P in frame {1} are [3.0 2.0 1.0]T. The position vector P is rotated about the x-axis by 60° in CCW direction. The sum of the coordinates of point Q (the new position of point P) will be . (Correct up to three decimal place)Correct answer is '5.367'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The coordinates of point P in frame {1} are [3.0 2.0 1.0]T. The position vector P is rotated about the x-axis by 60° in CCW direction. The sum of the coordinates of point Q (the new position of point P) will be . (Correct up to three decimal place)Correct answer is '5.367'. Can you explain this answer?.
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The coordinates of point P in frame {1} are [3.0 2.0 1.0]T. The position vector P is rotated about the x-axis by 60° in CCW direction. The sum of the coordinates of point Q (the new position of point P) will be . (Correct up to three decimal place)Correct answer is '5.367'. Can you explain this answer?, a detailed solution for The coordinates of point P in frame {1} are [3.0 2.0 1.0]T. The position vector P is rotated about the x-axis by 60° in CCW direction. The sum of the coordinates of point Q (the new position of point P) will be . (Correct up to three decimal place)Correct answer is '5.367'. Can you explain this answer? has been provided alongside types of The coordinates of point P in frame {1} are [3.0 2.0 1.0]T. The position vector P is rotated about the x-axis by 60° in CCW direction. The sum of the coordinates of point Q (the new position of point P) will be . (Correct up to three decimal place)Correct answer is '5.367'. Can you explain this answer? theory, EduRev gives you an
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