JEE Mains · Maths · STD 12 - 11. three dimension geometry
Let \(\overrightarrow{\mathrm{a}}=\hat{i}+2 \hat{j}+\hat{k}\) and \(\quad \overrightarrow{\mathrm{b}}=2 \hat{i}+7 \hat{j}+3 \hat{k} . \quad\) Let \(\mathrm{L}_1: \overrightarrow{\mathrm{r}}=(-\hat{i}+2 \hat{j}+\hat{k})+\lambda \overrightarrow{\mathrm{a}}, \lambda \in \mathbf{R}\) and \(\mathrm{L}_2: \overrightarrow{\mathrm{r}}=(\hat{j}+\hat{k})+\mu \overrightarrow{\mathrm{b}}, \mu \in \mathbf{R}\) be two lines. If the line \(\mathrm{L}_3\) passes through the point of intersection of \(\mathrm{L}_1\) and \(L_2\), and is parallel to \(\vec{a}+\vec{b}\), then \(L_3\) passes through the point :
- A \((5,17,4)\)
- B \((2,8,5)\)
- C \((8,26,12)\)
- D \((-1,-1,1)\)
Answer & Solution
Correct Answer
(C) \((8,26,12)\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & L_1: \overrightarrow{\mathrm{r}}=(-\hat{\mathrm{i}}+2 \hat{\mathrm{j}}+\hat{\mathrm{k}})+\lambda(\hat{\mathrm{i}}+2 \hat{\mathrm{j}}+\hat{\mathrm{k}}) \\ & \Rightarrow \overrightarrow{\mathrm{r}}=(\lambda-1) \hat{\mathrm{i}}+2(\lambda+1)…
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