Question

The plane containing the lines x=4+t, y=3−3t, z=1 and x=35, y=65, z=3−2s is:

A) Parallel to the XY-plane
B) Parallel to the XZ-plane
C) Parallel to the YZ-plane
D) Not parallel to any of the coordinate planes

Answer 1

The plane defined by the two given lines is not parallel to any coordinate plane because their direction vectors do not align with any of the axes.

Step-by-step explanation:

The student is asking about the orientation of a plane containing two given lines. To determine if this plane is parallel to any of the coordinate planes, we can use the direction vectors of the lines. The first line has a direction vector parallel to the vector (1, -3, 0), and the second line is stationary along the z-axis, with only the z-coordinate changing, indicating a direction vector (0, 0, -2). Since these two vectors are not parallel to any axis, the plane they define isn't parallel to any of the coordinate planes. Vectors parallel to the axes would have zeroes in all but one coordinate (indicating no movement along the other axes), which is not the case here. Therefore, the correct answer is D) Not parallel to any of the coordinate planes.