ویکٹر فیلڈ میں ایک نقطہ پر ویکٹر کا انحراف _____ مقدار ہے۔
A. A vector
B. Both A and B
C. None of these
D. A scalar
Explanation
Divergence of a vector field measures the rate at which a vector spreads out from a point, resulting in a scalar value . It is computed as the dot product of the del operator (∇) with the vector field, producing a single numerical value at each point. Show/Hide Explanation
A. None of these
B. 89
C. 80
D. 65
Explanation
To find the divergence, calculate:
div(f) = ∂/∂x (3x^2) + ∂/∂y (5xy) + ∂/∂z (xyz^3)
= 6x + 5x + 3xyz^2
At (1, 2, 3):
div(f) = 6(1) + 5(1) + 3(1)(2)(3)^2
= 6 + 5 + 54
= 65
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Explanation
For a vector field to be solenoidal, its divergence must be zero. The divergence of a vector field A = (x + 3y)i + (y - 2z)j + (x + mz)k is given by ∇ ⋅ A = ∂(x + 3y)/∂x + ∂(y - 2z)/∂y + ∂(x + mz)/∂z. Calculating the divergence : ∇ ⋅ A = 1 + 1 + m For the field to be solenoidal (∇ ⋅ A = 0), m must be -2.
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مندرجہ ذیل میں سے کون قیاس کی طرف جاتا ہے؟
A. All of these
B. Natural selection
C. Adaptation
D. Favorable genotypes
Explanation
Natural selection promotes the survival of individuals with advantageous traits, leading to genetic divergence. Favorable genotypes and adaptation help populations evolve differently, contributing to the formation of new species. Show/Hide Explanation
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