Find the torque of a force vec F =( hat i -2 overline j +3 vec k )N about a point O. The position vector of point of application of force about O is vec r =(2 overline i + overline j - overline k )m.
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Answer:
5i - 3j - 5k
Explanation:
We can determine the torque of a force by taking the cross product of the position vector and the force vector. The torque formula is:
Torque (τ) = r x F
In this case, the force vector F is (hat i - 2j + 3k) N, and the position vector r is (2i + j - k) m.
To calculate the torque, we need to perform the cross product:
r x F = | i j k |
| 2 1 -1 |
| 1 -2 3 |
Expanding the determinant:
r x F = (1*(-1) - (-2)*(3))i - (2*3 - 1*3)j + (2*(-2) - 1*1)k
= (-1 + 6)i - (6 - 3)j + (-4 - 1)k
= 5i - 3j - 5k
Thus, the torque of the force F about the point O is We can determine the torque of a force by taking the cross product of the position vector and the force vector. The torque formula is:
Torque (τ) = r x F
In this case, the force vector F is (hat i - 2j + 3k) N, and the position vector r is (2i + j - k) m.
To calculate the torque, we need to perform the cross product:
r x F = | i j k |
| 2 1 -1 |
| 1 -2 3 |
Expanding the determinant:
r x F = (1*(-1) - (-2)*(3))i - (2*3 - 1*3)j + (2*(-2) - 1*1)k
= (-1 + 6)i - (6 - 3)j + (-4 - 1)k
= 5i - 3j - 5k
Thus, the torque of the force F about the point O is 5i - 3j - 5k.
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