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The line r = (2, -1, 4) + λ(3, 0, 2), expressed in symmetric Cartesian form, is
A(x-2)/3 = (y+1)/0 = (z-4)/2
B(x+2)/3 = (y-1)/0 = (z+4)/2
C(x-2)/3 = y = (z-4)/2
D(x-3)/2 = y = (z-2)/4
Answer & Solution
Correct answer: A. (x-2)/3 = (y+1)/0 = (z-4)/2
1. The line passes through (2, -1, 4) with direction (3, 0, 2).
2. Symmetric form: (x - x₀)/a = (y - y₀)/b = (z - z₀)/c.
3. Substitute: (x-2)/3 = (y+1)/0 = (z-4)/2.
4. The middle term with denominator 0 encodes y = -1 in formal notation.
_Source: NCERT Class 12 Maths Part 2 Ch 11 "Three Dimensional Geometry", §11.3.1_
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