COMEDK · Maths · 34. Three Dimensional Geometry
The angle between the lines \(L_1: \dfrac{x-5}{\alpha}=\dfrac{y+2}{-5}=\dfrac{5 z+24}{5 \beta}\) and \(L_2: x=z, y=0\) is \(\dfrac{\pi}{4}\), then the value of \((4 \alpha \beta)\) is
- A 50
- B 25
- C \(\dfrac{5}{2}\)
- D \(\dfrac{25}{2}\)
Answer & Solution
Correct Answer
(A) 50
Step-by-step Solution
Detailed explanation
The line \(L_1\) is given by \(\dfrac{x-5}{\alpha} = \dfrac{y+2}{-5} = \dfrac{z + 24/5}{\beta}\). The direction vector of \(L_1\) is \(\vec{v_1} = \alpha \hat{i} - 5 \hat{j} + \beta \hat{k}\). The line \(L_2\) is given by \(x=z\) and \(y=0\). This can be written as…
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