QQuestion
If x ∝ y, y ∝ z and z ∝ x, then find the relation between the constants of variations.
✓Answer
x ∝ y implies x = k1 y.
y ∝ z implies y = k2 z.
z ∝ x implies z = k3 x.
Substitute y = k2 z into x = k1 y:
x = k1 (k2 z) = k1 k2 z.
Now substitute x = k1 k2 z into z = k3 x:
z = k3 (k1 k2 z).
Simplifying:
z = k1 k2 k3 z.
For this to hold true, k1 k2 k3 = 1.
Thus, the relation between the constants is:
k1 k2 k3 = 1.
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