Civil Engineering (CE) Exam  >  Civil Engineering (CE) Questions  >  The Cartesian coordinates of a point P in a r... Start Learning for Free
The Cartesian coordinates of a point P in a right-handed coordinate system are (1 ,1 , 1). The transformed coordinates of P due to a 45° clockwise rotation of the coordinate system about the positive x-axis are
  • a)
    (1,0, √2)
  • b)
    (1,0, -√2)
  • c)
    (-1,0, √2)
  • d)
    (-1,0, -√2)
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
The Cartesian coordinates of a point P in a right-handed coordinate sy...


Here answer is (a)
Free Test
Community Answer
The Cartesian coordinates of a point P in a right-handed coordinate sy...
Degree rotation about the z-axis are:

To find the transformed coordinates of point P due to a 45-degree rotation about the z-axis, we can use the rotation matrix for a 3D rotation about the z-axis:

| cosθ -sinθ 0 |
| sinθ cosθ 0 |
| 0 0 1 |

In this case, θ = 45 degrees.

Substituting the values into the rotation matrix, we have:

| cos45 -sin45 0 |
| sin45 cos45 0 |
| 0 0 1 |

Calculating the values, we get:

| √2/2 -√2/2 0 |
| √2/2 √2/2 0 |
| 0 0 1 |

Multiplying the rotation matrix by the Cartesian coordinates of point P (1, 1, 1), we have:

| √2/2 -√2/2 0 | | 1 | | (√2/2)(1) + (-√2/2)(1) + (0)(1) |
| √2/2 √2/2 0 | × | 1 | = | (√2/2)(1) + (√2/2)(1) + (0)(1) |
| 0 0 1 | | 1 | | (0)(1) + (0)(1) + (1)(1) |

Simplifying the calculations, we get:

| (√2/2)(1) + (-√2/2)(1) + (0)(1) | | 0 |
| (√2/2)(1) + (√2/2)(1) + (0)(1) | = | √2 |
| (0)(1) + (0)(1) + (1)(1) | | 1 |

Therefore, the transformed coordinates of point P due to a 45-degree rotation about the z-axis are (0, √2, 1).
Explore Courses for Civil Engineering (CE) exam

Similar Civil Engineering (CE) Doubts

Top Courses for Civil Engineering (CE)

The Cartesian coordinates of a point P in a right-handed coordinate system are (1 ,1 , 1). The transformed coordinates of P due to a 45° clockwise rotation of the coordinate system about the positive x-axis area)(1,0,√2)b)(1,0, -√2)c)(-1,0,√2)d)(-1,0, -√2)Correct answer is option 'A'. Can you explain this answer?
Question Description
The Cartesian coordinates of a point P in a right-handed coordinate system are (1 ,1 , 1). The transformed coordinates of P due to a 45° clockwise rotation of the coordinate system about the positive x-axis area)(1,0,√2)b)(1,0, -√2)c)(-1,0,√2)d)(-1,0, -√2)Correct answer is option 'A'. Can you explain this answer? for Civil Engineering (CE) 2024 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about The Cartesian coordinates of a point P in a right-handed coordinate system are (1 ,1 , 1). The transformed coordinates of P due to a 45° clockwise rotation of the coordinate system about the positive x-axis area)(1,0,√2)b)(1,0, -√2)c)(-1,0,√2)d)(-1,0, -√2)Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The Cartesian coordinates of a point P in a right-handed coordinate system are (1 ,1 , 1). The transformed coordinates of P due to a 45° clockwise rotation of the coordinate system about the positive x-axis area)(1,0,√2)b)(1,0, -√2)c)(-1,0,√2)d)(-1,0, -√2)Correct answer is option 'A'. Can you explain this answer?.
Solutions for The Cartesian coordinates of a point P in a right-handed coordinate system are (1 ,1 , 1). The transformed coordinates of P due to a 45° clockwise rotation of the coordinate system about the positive x-axis area)(1,0,√2)b)(1,0, -√2)c)(-1,0,√2)d)(-1,0, -√2)Correct answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for Civil Engineering (CE). Download more important topics, notes, lectures and mock test series for Civil Engineering (CE) Exam by signing up for free.
Here you can find the meaning of The Cartesian coordinates of a point P in a right-handed coordinate system are (1 ,1 , 1). The transformed coordinates of P due to a 45° clockwise rotation of the coordinate system about the positive x-axis area)(1,0,√2)b)(1,0, -√2)c)(-1,0,√2)d)(-1,0, -√2)Correct answer is option 'A'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of The Cartesian coordinates of a point P in a right-handed coordinate system are (1 ,1 , 1). The transformed coordinates of P due to a 45° clockwise rotation of the coordinate system about the positive x-axis area)(1,0,√2)b)(1,0, -√2)c)(-1,0,√2)d)(-1,0, -√2)Correct answer is option 'A'. Can you explain this answer?, a detailed solution for The Cartesian coordinates of a point P in a right-handed coordinate system are (1 ,1 , 1). The transformed coordinates of P due to a 45° clockwise rotation of the coordinate system about the positive x-axis area)(1,0,√2)b)(1,0, -√2)c)(-1,0,√2)d)(-1,0, -√2)Correct answer is option 'A'. Can you explain this answer? has been provided alongside types of The Cartesian coordinates of a point P in a right-handed coordinate system are (1 ,1 , 1). The transformed coordinates of P due to a 45° clockwise rotation of the coordinate system about the positive x-axis area)(1,0,√2)b)(1,0, -√2)c)(-1,0,√2)d)(-1,0, -√2)Correct answer is option 'A'. Can you explain this answer? theory, EduRev gives you an ample number of questions to practice The Cartesian coordinates of a point P in a right-handed coordinate system are (1 ,1 , 1). The transformed coordinates of P due to a 45° clockwise rotation of the coordinate system about the positive x-axis area)(1,0,√2)b)(1,0, -√2)c)(-1,0,√2)d)(-1,0, -√2)Correct answer is option 'A'. Can you explain this answer? tests, examples and also practice Civil Engineering (CE) tests.
Explore Courses for Civil Engineering (CE) exam

Top Courses for Civil Engineering (CE)

Explore Courses
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
10M+ students study on EduRev