JEE Mains · Maths · STD 12 - 11. three dimension geometry
Let the lines \(L _{1}: \overrightarrow{ r }=\lambda(\hat{ i }+2 \hat{ j }+3 \hat{ k }), \lambda \in R\) \(L _{2}: \overrightarrow{ r }=(\hat{ i }+3 \hat{ j }+\hat{ k })+\mu(\hat{ i }+\hat{ j }+5 \hat{ k }) ; \mu \in R\) intersect at the point \(S\). If a plane \(ax + by - z\) \(+d=0\) passes through \(S\) and is parallel to both the lines \(L _{1}\) and \(L _{2}\), then the value of \(a + b +\) \(d\) is equal to
- A \(9\)
- B \(4\)
- C \(5\)
- D \(3\)
Answer & Solution
Correct Answer
(C) \(5\)
Step-by-step Solution
Detailed explanation
\(\therefore\) equation of the plane \(\left|\begin{array}{ccc}x & y & z \\ 1 & 2 & 3 \\ 1 & 1 & 5 \end{array}\right|=0\) \(\Rightarrow 7 x-2 y-z=0 \) \(\therefore a+b+d=5\)
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