A plane has normal vector n = (1, 2, 2). A drone flies along direction d = (2, 1, -2). Will its path ever pierce the plane?

Yes, every line eventually crosses every plane

No, a line meets a plane unless it lies inside it

Yes, because d and n are not equal

Physics I / Lines, Planes, and Geometric Transformations

Practice question · Multiple choice

A plane has normal vector $\vec{n} = (1, 2, 2)$ . A drone flies along direction $\vec{d} = (2, 1, -2)$ . Will its path ever pierce the plane?

Hints

A direction lies within the plane’s orientation exactly when it is perpendicular to the normal.
Compute $\vec{d}\cdot\vec{n} = 2 + 2 - 4$ .

Show the answer

B. Not necessarily: the flight is parallel to the plane

Why

$\vec{d}\cdot\vec{n} = 0$ means the flight direction is perpendicular to the normal, hence parallel to the plane: the drone skims alongside forever (or lies inside it). One dot product settles an entire geometric question, the normal vector is the plane’s spokesperson.

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A plane has normal vector n⃗=(1,2,2)\vec{n} = (1, 2, 2)n=(1,2,2). A drone flies along direction d⃗=(2,1,−2)\vec{d} = (2, 1, -2)d=(2,1,−2). Will its path ever pierce the plane?

Practise Lines, Planes, and Geometric Transformations

More questions on Lines, Planes, and Geometric Transformations

A plane has normal vector $\vec{n} = (1, 2, 2)$ . A drone flies along direction $\vec{d} = (2, 1, -2)$ . Will its path ever pierce the plane?