Let a = i + j and b =2 i - k . The point of intersection of the lines r a = b a and r b =…
Mathematics · JEE Advanced · NTA Exams — Three Dimensional Geometry
Let \(\overrightarrow{\mathrm{a}}=\hat{\mathrm{i}}+\hat{\mathrm{j}} \text { and } \overrightarrow{\mathrm{b}}=2 \hat{\mathrm{i}}-\hat{\mathrm{k}}\). The point of intersection of the lines \(\overrightarrow{\mathrm{r}} \times \overrightarrow{\mathrm{a}}=\overrightarrow{\mathrm{b}} \times \overrightarrow{\mathrm{a}}\) and \(\overrightarrow{\mathrm{r}} \times \overrightarrow{\mathrm{b}}=\overrightarrow{\mathrm{a}} \times \overrightarrow{\mathrm{b}}\) is :
- \(-\hat{\mathrm{i}}+\hat{\mathrm{j}}+\hat{\mathrm{k}}\)
- \(3 \hat{i}-\hat{j}+\hat{k}\)
- \(3 \hat{i}+\hat{j}-\hat{k}\)
- \(\hat{\mathrm{i}}-\hat{\mathrm{j}}-\hat{\mathrm{k}}\)
Answer
(C) 3 i + j - k
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