JEE Mains · Maths · STD 12 - 11. three dimension geometry
If the lines \(\frac{x-1}{2}=\frac{2-y}{-3}=\frac{z-3}{\alpha}\) and \(\frac{x-4}{5}=\frac{y-1}{2}=\frac{z}{\beta}\) intersect, then the magnitude of the minimum value of \(8 \alpha \beta\) is \(...............\).
- A \(16\)
- B \(14\)
- C \(18\)
- D \(12\)
Answer & Solution
Correct Answer
(C) \(18\)
Step-by-step Solution
Detailed explanation
If the lines \(\frac{x-1}{2}=\frac{2-y}{-3}=\frac{z-3}{\alpha}\) And \(\frac{x-4}{5}=\frac{y-1}{2}=\frac{z}{\beta}\) intersect Point on first line \((1,2,3)\) and point on second line \((4,1,0)\). Vector joining both points is \(-3 \hat{i}+\hat{j}+3 \hat{k}\) Now vector along…
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