JEE Mains · Maths · STD 12 - 11. three dimension geometry
Let the image of the point \((1,0,7)\) in the line \(\frac{x}{1}=\frac{y-1}{2}=\frac{z-2}{3}\) be the point \((\alpha, \beta, \gamma)\). Then which one of the following points lies on the line passing through \((\alpha, \beta, \gamma)\) and making angles \(\frac{2 \pi}{3}\) and \(\frac{3 \pi}{4}\) with \(y\)-axis and \(z\)-axis respectively and an acute angle with \(\mathrm{x}\)-axis?
- A \((1,-2,1+\sqrt{2})\)
- B \((1,2,1-\sqrt{2})\)
- C \((3,4,3-2 \sqrt{2})\)
- D \((3,-4,3+2 \sqrt{2})\)
Answer & Solution
Correct Answer
(C) \((3,4,3-2 \sqrt{2})\)
Step-by-step Solution
Detailed explanation
\(L_1=\frac{x}{1}=\frac{y-1}{2}=\frac{z-2}{3}=\lambda\) \( \mathrm{M}(\lambda, 1+2 \lambda, 2+3 \lambda) \) \( \overrightarrow{\mathrm{PM}}=(\lambda-1) \hat{i}+(1+2 \lambda) \hat{j}+(3 \lambda-5) \hat{k}\) \(\overrightarrow{\mathrm{PM}}\) is perpendicular to line…
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