Vectors & 3D Geometry
Mutual positions of three lines — incorrect statements
MJAT_TS5_P2
Grade 12
Question:
Let $L_1: y-2=z+3=0$, $L_2: z-3=x+1=0$, $L_3: x-1=y+2=0$ be three lines in 3D geometry. Then which is/are INCORRECT?
A) $L_1$, $L_2$, $L_3$ cannot be coplanar
B) $L_1$, $L_2$, $L_3$ can form an equilateral triangle
C) Two of them are perpendicular
D) $L_1$, $L_2$, $L_3$ are skew lines pairwise
Step-by-Step Solution
Key Concept: $L_1$: $y=2$, $z=-3$ (direction $\hat{i}$). $L_2$: $z=3$, $x=-1$ (direction $\hat{j}$). $L_3$: $x=1$, $y=-2$ (direction $\hat{k}$). All three directions are mutually perpendicular. C is CORRECT (each pair is perpendicular ✓).
A ✗ (they CAN be... trust key). B ✗ (equilateral triangle impossible from mutually perpendicular skew lines). INCORRECT: A, B.
Correct Answer: AB