Question

Shortest distance between the lines \( \vec{r} = (8 + 3\lambda)\hat{i} - (9 + 16\lambda)\hat{j} + (10 + 7\lambda)\hat{k} \) and \( \vec{r} = 15\hat{i} + 29\hat{j} + 5\hat{k} + \mu(3\hat{i} + 8\hat{j} - 5\hat{k}) \) is

• A. 3 units
• B. 7 units
• C. 14 units
• D. 2 units

Hint:

The shortest distance between two skew lines can be found using the formula \( D = \frac{|(\vec{b}_2 - \vec{b}_1) \cdot (\vec{a}_1 \times \vec{a}_2)|}{|\vec{a}_1 \times \vec{a}_2|} \), where \( \vec{a}_1 \) and \( \vec{a}_2 \) are the direction vectors of the lines.

Answer 1

The Correct Option is C