3D Geometry
Angle between projections of non-perpendicular lines on a plane
Grade Class 12
Question:
Let $L_1$, $L_2$ be two distinct lines such that $L_1$ and $L_2$ are not perpendicular. Let $P$ be a plane such that $L_1$ and $L_2$ are not perpendicular to $P$. Let $L_3$ and $L_4$ be projections of $L_1$ and $L_2$ on plane $P$ respectively. If $\theta$ be angle between $L_3$ and $L_4$ then $\theta$ CANNOT be equal to
$0$
$\dfrac{\pi}{3}$
$\dfrac{\pi}{2}$
none of these
Step-by-Step Solution
Key Concept: $\theta$ can be any value in $[0, \pi/2]$ by choosing the plane $P$ appropriately. In particular $\theta=0$ (parallel projections), $\pi/3$, and $\pi/2$ are all achievable.
$\theta\in[0,\pi/2]$; all three listed values are achievable, so the answer is 'none of these'.
Correct Answer: 4