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AP EAMCET · Maths · Three Dimensional Geometry

If the line with direction ratios \((1, \alpha, \beta)\) is perpendicular to the line with direction ratios \((-1,2,1)\) and parallel to the line with direction ratios \((\alpha, 1, \beta)\), then \((\alpha, \beta)\) is

  1. A \((-1,-1)\)
  2. B \((1,-1)\)
  3. C \((-1,3)\)
  4. D \((1,1)\)
Verified Solution

Answer & Solution

Correct Answer

(B) \((1,-1)\)

Step-by-step Solution

Detailed explanation

Since line with \(d r^{\prime} s(1, u, \beta)\) is perpendicular to line with \(d r^{\prime} s(-1,2,1)-1+2 \alpha+\beta=0 \Rightarrow 2 \alpha+\beta=1\) Also, \(\lambda(\hat{i}+\alpha \tilde{j}+\beta \hat{k})=\alpha \hat{i}+\hat{j}+\beta \vec{k}\) \(\lambda=\alpha\) and…