Question

The shortest distance between the lines \( 1 + x = 2y = -12z \) and \( x = y + 2 = 6z - 6 \) is

• A. 1 unit
• B. 4 units
• C. 2 units
• D. 3 units

Hint:

To find the shortest distance between two skew lines, use the formula involving the cross product and the vector between points on each line.

Answer 1

The Correct Option is C

Step 1: Parametrize the equations.
For the first line, the direction ratios are \( (1, 2, -12) \), and for the second line, the direction ratios are \( (1, 1, 6) \).
Step 2: Use the formula for the shortest distance.
The formula for the shortest distance between two skew lines is: \[ d = \frac{|(\vec{a_2} - \vec{a_1}) \cdot (\vec{d_1} \times \vec{d_2})|}{|\vec{d_1} \times \vec{d_2}|} \] By substituting the values of direction ratios, we calculate the shortest distance to be \( 2 \) units.
Step 3: Conclusion.
The correct answer is (C) 2 units.