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We need to apply vector math sometimes in the calculation of stability of equilibrium configurations. So the coordinate of the Force vector AB is A (2, 0, 2) and B (-2, 3.46, 3). It has a magnitude of 750N. Which is the best Cartesian representation of the vector AB?
- a)-557i + 482j + 139k N
- b)-557i – 482j + 139k N
- c)-557i + 482j – 139k N
- d)557i – 482j – 139k N
Correct answer is option 'A'. Can you explain this answer?
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We need to apply vector math sometimes in the calculation of stability...
First try to make the unit vector of AB. Then you will get the Cartesian form of unit vector, after that just multiply 750 scalar quantity with it. Which means you are first taking out the desired direction and then multiplying the scalar to get the desired vector in desired direction.
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We need to apply vector math sometimes in the calculation of stability...
Given Data:
Coordinates of point A: (2, 0, 2)
Coordinates of point B: (-2, 3.46, 3)
Magnitude of vector AB: 750N
Calculating Vector AB:
To find the vector AB, we subtract the coordinates of point A from the coordinates of point B.
AB = B - A
AB = (-2 - 2)i + (3.46 - 0)j + (3 - 2)k
AB = -4i + 3.46j + k
Calculating Magnitude of Vector AB:
The magnitude of a vector in 3D space is calculated using the formula:
|AB| = √(x^2 + y^2 + z^2)
|AB| = √((-4)^2 + 3.46^2 + 1^2)
|AB| = √(16 + 11.9716 + 1)
|AB| = √28.9716
|AB| ≈ 5.386
Comparing with Given Magnitude:
The given magnitude of vector AB is 750N, which does not match the calculated magnitude of approximately 5.386. Therefore, the correct representation of vector AB in Cartesian form is:
-557i + 482j + 139k N
Therefore, option A is the best Cartesian representation of the vector AB.
Coordinates of point A: (2, 0, 2)
Coordinates of point B: (-2, 3.46, 3)
Magnitude of vector AB: 750N
Calculating Vector AB:
To find the vector AB, we subtract the coordinates of point A from the coordinates of point B.
AB = B - A
AB = (-2 - 2)i + (3.46 - 0)j + (3 - 2)k
AB = -4i + 3.46j + k
Calculating Magnitude of Vector AB:
The magnitude of a vector in 3D space is calculated using the formula:
|AB| = √(x^2 + y^2 + z^2)
|AB| = √((-4)^2 + 3.46^2 + 1^2)
|AB| = √(16 + 11.9716 + 1)
|AB| = √28.9716
|AB| ≈ 5.386
Comparing with Given Magnitude:
The given magnitude of vector AB is 750N, which does not match the calculated magnitude of approximately 5.386. Therefore, the correct representation of vector AB in Cartesian form is:
-557i + 482j + 139k N
Therefore, option A is the best Cartesian representation of the vector AB.
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We need to apply vector math sometimes in the calculation of stability of equilibrium configurations. So the coordinate of the Force vector AB is A (2, 0, 2) and B (-2, 3.46, 3). It has a magnitude of 750N. Which is the best Cartesian representation of the vector AB?a)-557i + 482j + 139k Nb)-557i – 482j + 139k Nc)-557i + 482j – 139k Nd)557i – 482j – 139k NCorrect answer is option 'A'. Can you explain this answer?
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We need to apply vector math sometimes in the calculation of stability of equilibrium configurations. So the coordinate of the Force vector AB is A (2, 0, 2) and B (-2, 3.46, 3). It has a magnitude of 750N. Which is the best Cartesian representation of the vector AB?a)-557i + 482j + 139k Nb)-557i – 482j + 139k Nc)-557i + 482j – 139k Nd)557i – 482j – 139k NCorrect answer is option 'A'. 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 We need to apply vector math sometimes in the calculation of stability of equilibrium configurations. So the coordinate of the Force vector AB is A (2, 0, 2) and B (-2, 3.46, 3). It has a magnitude of 750N. Which is the best Cartesian representation of the vector AB?a)-557i + 482j + 139k Nb)-557i – 482j + 139k Nc)-557i + 482j – 139k Nd)557i – 482j – 139k NCorrect answer is option 'A'. 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 We need to apply vector math sometimes in the calculation of stability of equilibrium configurations. So the coordinate of the Force vector AB is A (2, 0, 2) and B (-2, 3.46, 3). It has a magnitude of 750N. Which is the best Cartesian representation of the vector AB?a)-557i + 482j + 139k Nb)-557i – 482j + 139k Nc)-557i + 482j – 139k Nd)557i – 482j – 139k NCorrect answer is option 'A'. Can you explain this answer?.
We need to apply vector math sometimes in the calculation of stability of equilibrium configurations. So the coordinate of the Force vector AB is A (2, 0, 2) and B (-2, 3.46, 3). It has a magnitude of 750N. Which is the best Cartesian representation of the vector AB?a)-557i + 482j + 139k Nb)-557i – 482j + 139k Nc)-557i + 482j – 139k Nd)557i – 482j – 139k NCorrect answer is option 'A'. 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 We need to apply vector math sometimes in the calculation of stability of equilibrium configurations. So the coordinate of the Force vector AB is A (2, 0, 2) and B (-2, 3.46, 3). It has a magnitude of 750N. Which is the best Cartesian representation of the vector AB?a)-557i + 482j + 139k Nb)-557i – 482j + 139k Nc)-557i + 482j – 139k Nd)557i – 482j – 139k NCorrect answer is option 'A'. 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 We need to apply vector math sometimes in the calculation of stability of equilibrium configurations. So the coordinate of the Force vector AB is A (2, 0, 2) and B (-2, 3.46, 3). It has a magnitude of 750N. Which is the best Cartesian representation of the vector AB?a)-557i + 482j + 139k Nb)-557i – 482j + 139k Nc)-557i + 482j – 139k Nd)557i – 482j – 139k NCorrect answer is option 'A'. Can you explain this answer?.
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