Question

Analyze the definition below and complete the instructions that follow.

Parallel planes are two planes that will never intersect one another.
Identify p and q in the definition above.
A. p: parallel planes are two planes; q: never intersect one another.
B. p: two lines intersect one another; q: two planes are not parallel.
C. p: two planes are parallel; q: they never intersect one another.
D. p: there are two planes; q: two planes are parallel.

Answer 1

The correct identification of p and q in the definition of parallel planes is 'C': p corresponds to 'two planes are parallel' and q to 'they never intersect one another'. In vector terms, parallel vectors have identical directions, while orthogonal vectors are perpendicular, differing by 90°.

Step-by-step explanation:

Analyzing the definition of parallel planes and identifying p and q, we determine the correct pairing to be C. Here, p: two planes are parallel; this part of the definition specifies the relationship between the two planes. q: they never intersect one another; this part explains the consequence of the planes being parallel. Reviewing other concepts, two vectors that have identical directions are considered to be parallel vectors. Conversely, two vectors with directions perpendicular to each other are known as orthogonal vectors, often synonymous with perpendicular vectors. Orthogonal vectors differ by exactly 90°. The parallelogram rule assists in the geometric construction of the vector sum in a plane.