JEE Mains · Maths · STD 12 - 11. three dimension geometry
Let \(P_{1}: \vec{r} \cdot(2 \hat{ i }+\hat{ j }-3 \hat{ k })=4\) be a plane. Let \(P_{2}\) be another plane which passes through the points \((2,-\) \(3,2)(2,-2,-3)\) and \((1,-4,2)\). If the direction ratios of the line of intersection of \(P_{1}\) and \(P_{2}\) be \(16\) , \(\alpha, \beta\), then the value of \(\alpha+\beta\) is equal to
- A \(27\)
- B \(28\)
- C \(29\)
- D \(30\)
Answer & Solution
Correct Answer
(B) \(28\)
Step-by-step Solution
Detailed explanation
\(P_{1}: \vec{r} \cdot(2 \hat{ i }+\hat{ j }-3 \hat{ k })=4\) \(P_{1}: 2 x+y-3 z=4\) \(P_{2}\left|\begin{array}{ccc} x-2 & y+3 & z-2 \\ 0 & 1 & -5 \\ -1 & -1 & 0 \end{array}\right|=0\) \(\Rightarrow-5 x+5 y+z+23=0\) Let \(a, b, c\) be the \(d'rs\) of line of intersection Then…
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