Mathematics

Mathematics

Problem

Consider the following four pairs of line in Column I and match them with one or more entries in Column II.
Column IColumn II
(A) L1:x=1+t,y=t,z=2−5tL_1: x = 1 + t, y = t, z = 2 - 5t<br>L2:r=(2,1,−3)+λ(2,2,−10)L_2: r = (2, 1, -3) + \lambda(2, 2, -10)(p) non-coplanar lines
(B) L1:x−12=y−32=z−2−1L_1: \frac{x-1}{2} = \frac{y-3}{2} = \frac{z-2}{-1}<br>L2:x−21=y−6−1=z+2−1L_2: \frac{x-2}{1} = \frac{y-6}{-1} = \frac{z+2}{-1}(q) lines lie in a unique plane
(C) L1:x=−6t,y=1+9t,z=−3tL_1: x = -6t, y = 1 + 9t, z = -3t<br>L2:x=1+2s,y=4−3s,z=sL_2: x = 1 + 2s, y = 4 - 3s, z = s(r) infinite planes containing both the lines
(D) L1:x1=y−12=z−23L_1: \frac{x}{1} = \frac{y-1}{2} = \frac{z-2}{3}<br>L2:x−3−4=y−2−3=z−12L_2: \frac{x-3}{-4} = \frac{y-2}{-3} = \frac{z-1}{2}(s) lines are not intersecting at a unique point

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