MHT CET · Maths · Three Dimensional Geometry
The line passing through the point \((5,1, a)\) and \((3, b, 1)\) crosses the yz-plane at \(\left(0, \frac{17}{2}, \frac{-13}{2}\right)\), then the value of \(2 a+3 \mathrm{~b}\) is
- A \(10\)
- B \(12\)
- C \(22\)
- D \(24\)
Answer & Solution
Correct Answer
(D) \(24\)
Step-by-step Solution
Detailed explanation
\(0 = 5 + \lambda(3-5) \Rightarrow 0 = 5 - 2\lambda \Rightarrow \lambda = \frac{5}{2}\) \(\frac{17}{2} = 1 + \lambda(b-1) \Rightarrow \frac{17}{2} = 1 + \frac{5}{2}(b-1) \Rightarrow 17 = 2 + 5(b-1) \Rightarrow 15 = 5(b-1) \Rightarrow b-1 = 3 \Rightarrow b = 4\)
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