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Spheres of unit diameter are centered at (l,m,n) where l, m, and n take every possible integer values. The distance between two spheres is computed from the center of one sphere to the center of the other sphere. For a given sphere, x is the distance to its nearest sphere and y is the distance to its next nearest sphere. The value of y/x is:
- 2√2
- 1/√2
- √2
- 2
Correct answer: √2
Solution
The distance between the centers of two adjacent spheres is 2 units, while the distance to the next nearest sphere, which is diagonally adjacent, is √2 units. Therefore, the ratio y/x, where y is the distance to the next nearest sphere and x is the distance to the nearest sphere, simplifies to √2.
Related GATE Engineering Mathematics questions
- A vector field p and a scalar field r are given by
p = (2x² - 3xy + z²) î + (2y² - 3yz + x²) ĵ + (2z² - 3xz + x²) k̂
r = 6x² + 4y² - z² - 9xyz - 2xy + 3xz - yz
Consider the statements P and Q.
P: Curl of the gradient of the scalar field r is a null vector.
Q: Divergence of curl of the vector field p is zero.
Which one of the following options is CORRECT?
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- Three vectors p, q and r are given as p = î + ĵ + k̂, q = î + 2ĵ + 3k̂, r = 2î + 3ĵ + 4k̂. Which of the following is/are CORRECT?
- If a vector field V is related to another vector field A through V = ∇ × A, which of the following is true? Note: C and S_c refer to any closed contour and any surface whose boundary is C.
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