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If the force vector F is having its x-axis component being equal to Z N, y-axis component be X N and z-axis component be Y N then vector F is best represented by?
- a)Xi + Yj + Zk
- b)Yi + Xj + Zk
- c)Zi + Yj + Xk
- d)Zi + Xj + Yk
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
If the force vector F is having its x-axis component being equal to Z ...
It is given that x, y and z-axis components are Z, X and Y respectively. Thus, just by placing the right coordinates we get option d to be correct. Here just the interchange of the axis’s representor with their respective axis is creating confusion. Which must be figured out.
Most Upvoted Answer
If the force vector F is having its x-axis component being equal to Z ...
To determine the best representation of the force vector F, we need to consider the given components of the force vector along the x-axis, y-axis, and z-axis.
The force vector F can be represented as a sum of its components along the x, y, and z axes:
F = Xi + Yj + Zk
Here, i, j, and k represent the unit vectors along the x, y, and z axes, respectively.
Explanation:
1. Identify the given components
- x-axis component = Z N
- y-axis component = X N
- z-axis component = Y N
2. Assign the components to the corresponding unit vectors
- x-axis component = ZN * i
- y-axis component = XN * j
- z-axis component = YN * k
3. Write the force vector F using the assigned components
- F = ZN * i + XN * j + YN * k
4. Combine the terms and rearrange to find the best representation
- F = Zi + Xj + Yk
Therefore, the best representation of the force vector F is option D: Zi + Xj + Yk.
In this representation, the force vector is written as a sum of its components along the x, y, and z axes, with the corresponding unit vectors i, j, and k. This representation follows the standard convention for expressing vectors in terms of their components.
The force vector F can be represented as a sum of its components along the x, y, and z axes:
F = Xi + Yj + Zk
Here, i, j, and k represent the unit vectors along the x, y, and z axes, respectively.
Explanation:
1. Identify the given components
- x-axis component = Z N
- y-axis component = X N
- z-axis component = Y N
2. Assign the components to the corresponding unit vectors
- x-axis component = ZN * i
- y-axis component = XN * j
- z-axis component = YN * k
3. Write the force vector F using the assigned components
- F = ZN * i + XN * j + YN * k
4. Combine the terms and rearrange to find the best representation
- F = Zi + Xj + Yk
Therefore, the best representation of the force vector F is option D: Zi + Xj + Yk.
In this representation, the force vector is written as a sum of its components along the x, y, and z axes, with the corresponding unit vectors i, j, and k. This representation follows the standard convention for expressing vectors in terms of their components.
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