Question

Find the square of the distance of the point \( (5, 6, 7) \) from the line \( \frac{x-2}{2} = \frac{y-5}{3} = \frac{z-2}{4} \):

Hint:

To avoid solving for \( \lambda \), you can use the vector cross product formula: \( d = \frac{|\vec{AP} \times \vec{b}|}{|\vec{b}|} \), where \( A \) is a point on the line and \( \vec{b} \) is the direction vector.

Answer 1

Correct Answer: 6