Question #41737

This question tests the geometric interpretation of the cross product and the strict definition of a line.

Students routinely solve the scalar triple product $[\\vec{n}, \\vec{p}, \\vec{q}] = 0$ to find when the direction vector is coplanar with the plane.

However, they often forget that if $\\vec{p}$ and $\\vec{q}$ are collinear, their cross product is the null vector $\\vec{0}$.

A line cannot have a null direction vector.

The modulus creates a piecewise condition where one of the algebraic solutions ($\\lambda = 1/2$) corresponds exactly to the case where $\\vec{p} = \\vec{q}$, yielding $\\vec{d} = \\vec{0}$.

Blindly summing the roots of the scalar triple product equation leads to the incorrect trap answer 7/2.