Mathematics · JEE | THREE DIMENSIONAL GEOMETRY

Match List-I with List-II: List-I (Line / Parameter) List-II (Value / Form) A Direction ratios of line \( \frac{x-5}{3} = \frac{y+4}{7} = \frac{z-6}{2} \) I \( \frac{\sqrt{293}}{7} \) B Distance between lines \( \vec{r} = (\hat{i}+2\hat{j}-4\hat{k})+\lambda(2\hat{i}+3\hat{j}+6\hat{k}) \) and \( \vec{r} = (3\hat{i}+3\hat{j}-5\hat{k})+\mu(2\hat{i}+3\hat{j}+6\hat{k}) \) II \( (3, 7, 2) \) C Value of \( k \) if lines with d.r. \( (-3, 2k, 2) \) and \( (3k, 1, -5) \) are perpendicular III \( -\frac{10}{7} \) D Shortest distance between lines with \( \vec{b}_1 \times \vec{b}_2 = 8\hat{i}+8\hat{j}+4\hat{k} \) and \( \vec{a}_2 - \vec{a}_1 = -10\hat{i}-2\hat{j}-3\hat{k} \) IV 9 Choose the correct answer from the options given below:

1. A
   A-(II), B-(I), C-(IV), D-(III)
2. B
   A-(II), B-(I), C-(III), D-(IV)
3. C
   A-(I), B-(II), C-(III), D-(IV)
4. D
   A-(III), B-(I), C-(II), D-(IV)