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Find the Gauss value for a position vector in Cartesian system from the origin to one unit in three dimensions.
- a)0
- b)3
- c)-3
- d)1
Correct answer is option 'B'. Can you explain this answer?
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Find the Gauss value for a position vector in Cartesian system from th...
Answer: b
Explanation: The position vector in Cartesian system is given by R = x i + y j + z k. Div(R) = 1 + 1 + 1 = 3. By divergence theorem, ∫∫∫3.dV, where V is a cube with x = 0->1, y = 0->1 and z = 0->1. On integrating, we get 3 units.
Explanation: The position vector in Cartesian system is given by R = x i + y j + z k. Div(R) = 1 + 1 + 1 = 3. By divergence theorem, ∫∫∫3.dV, where V is a cube with x = 0->1, y = 0->1 and z = 0->1. On integrating, we get 3 units.
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Find the Gauss value for a position vector in Cartesian system from th...
The Gauss value for a position vector in a Cartesian system refers to the magnitude of the vector. In this case, we are given a position vector that starts from the origin and extends to a point one unit away in three dimensions.
To find the Gauss value, we need to calculate the magnitude of the vector using the Pythagorean theorem. The Pythagorean theorem states that for a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. In this case, the position vector forms a right triangle with the x, y, and z coordinates representing the sides of the triangle.
Let's denote the position vector as R, with components Rx, Ry, and Rz. Using the Pythagorean theorem, the magnitude of the vector can be calculated as follows:
|R| = sqrt(Rx^2 + Ry^2 + Rz^2)
Since the position vector extends one unit in each dimension, we can substitute the values into the equation:
|R| = sqrt(1^2 + 1^2 + 1^2)
= sqrt(3)
Therefore, the Gauss value for the position vector is sqrt(3), which is approximately 1.732.
So, the correct answer is option 'B'.
To find the Gauss value, we need to calculate the magnitude of the vector using the Pythagorean theorem. The Pythagorean theorem states that for a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. In this case, the position vector forms a right triangle with the x, y, and z coordinates representing the sides of the triangle.
Let's denote the position vector as R, with components Rx, Ry, and Rz. Using the Pythagorean theorem, the magnitude of the vector can be calculated as follows:
|R| = sqrt(Rx^2 + Ry^2 + Rz^2)
Since the position vector extends one unit in each dimension, we can substitute the values into the equation:
|R| = sqrt(1^2 + 1^2 + 1^2)
= sqrt(3)
Therefore, the Gauss value for the position vector is sqrt(3), which is approximately 1.732.
So, the correct answer is option 'B'.
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Find the Gauss value for a position vector in Cartesian system from the origin to one unit in three dimensions.a)0b)3c)-3d)1Correct answer is option 'B'. Can you explain this answer?
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