Answer
b) and c)
Work Step by Step
Compute two vectors on the plane
Let’s define two vectors lying on the plane:
Vector A =(1,1,1)-(1,0,0)=(0,1,1)
Vector B =(1,0,2)-(1,0,0)=(0,0,2)
Compute the normal vector:
Take the cross product of A and B:
$\overrightarrow{N}=\overrightarrow{A}\times \overrightarrow{B}=\begin{vmatrix}i&j&k\\0&1&1\\0&0&2\end{vmatrix}=(2,0,0)$
Analyze each line segment
Let’s compute the direction vector of each segment and compare it to the normal vector:
a. From (1,0,0) to (1,1,0)
Direction: (0,1,0)
Not parallel to (2,0,0)
→ Not normal
b. From (1,1,1) to (2,1,1)
Direction: (1,0,0)
Parallel to (2,0,0)
→ Normal
c. From (1,0,2) to (0,0,2)
Direction: (-1,0,0)
Parallel to (2,0,0)
→ Normal
d. From (1,0,0) to (1,1,1)
Direction: (0,1,1)
Not parallel to (2,0,0)
→ Not normal
The answer is: b) and c).
