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Which statement is right for force vector F = Ai + Bj + Ck?
- a)In rectangular components representation of any vector we have vector F = Ai + Bj + Ck
- b)In rectangular components representation of any vector we have vector F = Ax + By + Cz
- c)In rectangular components representation of any vector we have vector F = Fx + Fy + Fz
- d)In rectangular components representation of any vector we have vector F = Fi + Fj + Fk
Correct answer is option 'C'. Can you explain this answer?
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Which statement is right for force vector F = Ai + Bj + Ck?a)In rectan...
As given the vector is F = Ai + Bj + Ck, this implies that the x ,y and z-axis components of this vector is A, B and C respectively. But, in rectangular components representation of any vector, the vector is written as F = Fx + Fy + Fz.
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Which statement is right for force vector F = Ai + Bj + Ck?a)In rectan...
Rectangular Components Representation of Vector F
In the rectangular coordinate system, any vector can be represented by its components along the x, y, and z axes. For the force vector F = Ai Bj Ck, the rectangular components representation is as follows:
Vector F = Fx Fy Fz
Explanation
- The x-component of vector F is represented by Fx, which is equal to the coefficient A of the i unit vector. The i unit vector is a vector in the x-direction with a magnitude of 1. Therefore, the x-component of vector F is A.
- Similarly, the y-component of vector F is represented by Fy, which is equal to the coefficient B of the j unit vector. The j unit vector is a vector in the y-direction with a magnitude of 1. Therefore, the y-component of vector F is B.
- Likewise, the z-component of vector F is represented by Fz, which is equal to the coefficient C of the k unit vector. The k unit vector is a vector in the z-direction with a magnitude of 1. Therefore, the z-component of vector F is C.
- Hence, the rectangular components representation of vector F is Fx Fy Fz, where Fx = A, Fy = B, and Fz = C.
Conclusion
In summary, option 'C' is the right statement for the force vector F = Ai Bj Ck. The rectangular components representation of any vector is given by its components along the x, y, and z axes. For the force vector F, its rectangular components representation is Fx Fy Fz, where Fx = A, Fy = B, and Fz = C.
In the rectangular coordinate system, any vector can be represented by its components along the x, y, and z axes. For the force vector F = Ai Bj Ck, the rectangular components representation is as follows:
Vector F = Fx Fy Fz
Explanation
- The x-component of vector F is represented by Fx, which is equal to the coefficient A of the i unit vector. The i unit vector is a vector in the x-direction with a magnitude of 1. Therefore, the x-component of vector F is A.
- Similarly, the y-component of vector F is represented by Fy, which is equal to the coefficient B of the j unit vector. The j unit vector is a vector in the y-direction with a magnitude of 1. Therefore, the y-component of vector F is B.
- Likewise, the z-component of vector F is represented by Fz, which is equal to the coefficient C of the k unit vector. The k unit vector is a vector in the z-direction with a magnitude of 1. Therefore, the z-component of vector F is C.
- Hence, the rectangular components representation of vector F is Fx Fy Fz, where Fx = A, Fy = B, and Fz = C.
Conclusion
In summary, option 'C' is the right statement for the force vector F = Ai Bj Ck. The rectangular components representation of any vector is given by its components along the x, y, and z axes. For the force vector F, its rectangular components representation is Fx Fy Fz, where Fx = A, Fy = B, and Fz = C.
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Which statement is right for force vector F = Ai + Bj + Ck?a)In rectangular components representation of any vector we have vector F = Ai + Bj + Ckb)In rectangular components representation of any vector we have vector F = Ax + By + Czc)In rectangular components representation of any vector we have vector F = Fx + Fy + Fzd)In rectangular components representation of any vector we have vector F = Fi + Fj + FkCorrect answer is option 'C'. Can you explain this answer?
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Which statement is right for force vector F = Ai + Bj + Ck?a)In rectangular components representation of any vector we have vector F = Ai + Bj + Ckb)In rectangular components representation of any vector we have vector F = Ax + By + Czc)In rectangular components representation of any vector we have vector F = Fx + Fy + Fzd)In rectangular components representation of any vector we have vector F = Fi + Fj + FkCorrect answer is option 'C'. 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 Which statement is right for force vector F = Ai + Bj + Ck?a)In rectangular components representation of any vector we have vector F = Ai + Bj + Ckb)In rectangular components representation of any vector we have vector F = Ax + By + Czc)In rectangular components representation of any vector we have vector F = Fx + Fy + Fzd)In rectangular components representation of any vector we have vector F = Fi + Fj + FkCorrect answer is option 'C'. 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 Which statement is right for force vector F = Ai + Bj + Ck?a)In rectangular components representation of any vector we have vector F = Ai + Bj + Ckb)In rectangular components representation of any vector we have vector F = Ax + By + Czc)In rectangular components representation of any vector we have vector F = Fx + Fy + Fzd)In rectangular components representation of any vector we have vector F = Fi + Fj + FkCorrect answer is option 'C'. Can you explain this answer?.
Which statement is right for force vector F = Ai + Bj + Ck?a)In rectangular components representation of any vector we have vector F = Ai + Bj + Ckb)In rectangular components representation of any vector we have vector F = Ax + By + Czc)In rectangular components representation of any vector we have vector F = Fx + Fy + Fzd)In rectangular components representation of any vector we have vector F = Fi + Fj + FkCorrect answer is option 'C'. 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 Which statement is right for force vector F = Ai + Bj + Ck?a)In rectangular components representation of any vector we have vector F = Ai + Bj + Ckb)In rectangular components representation of any vector we have vector F = Ax + By + Czc)In rectangular components representation of any vector we have vector F = Fx + Fy + Fzd)In rectangular components representation of any vector we have vector F = Fi + Fj + FkCorrect answer is option 'C'. 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 Which statement is right for force vector F = Ai + Bj + Ck?a)In rectangular components representation of any vector we have vector F = Ai + Bj + Ckb)In rectangular components representation of any vector we have vector F = Ax + By + Czc)In rectangular components representation of any vector we have vector F = Fx + Fy + Fzd)In rectangular components representation of any vector we have vector F = Fi + Fj + FkCorrect answer is option 'C'. Can you explain this answer?.
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