If a line (x+1)/p = (y-1)/q = (z-2)/r where p = 2q = 3r, makes an angle θ with the positive direction of y-axis, then what is cos2θ equal to?

Let r = 1, then q = 3/2, p = 3. Wait: p = 2q = 3r means p=3r and q = 3r/2. Take r=2: p=6, q=3, r=2. Direction ratios (6,3,2), magnitude √(36+9+4) = 7. cosθ = 3/7 (with y-axis). cos2θ = 2cos²θ - 1 = 2(9/49) - 1 = 18/49 - 49/49 = -31/49. Hmm answer is (a). Let me recheck — with p = 2q = 3r, let common value = 6: p=6, q=3, r=2. cosθ = q/√(p²+q²+r²) = 3/7. cos2θ = 2(9/49)-1 = -31/49. So answer is (a) -31/49.