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Let P(1) and P(2) be two planes containi...

Let `P_(1) and P_(2)` be two planes containing the lines `L_(2) and L_(2)` respectively.
STATEMENT-1 : If `P_(1) and P_(2)` are parallel then `L_(1) and L_(2)` must be parallel.
and
STATEMENT-2 : If `P_(1) and P_(2)` are parallel the `L_(1) and L_(2)` may not have a common point.

A

Statement-1 is True, Statement-2 is true, Statement- is a correct explanation for Statement -1

B

Statement-1 is True, Statement-2 is true, Statement- is NOT a correct explanation for Statement -1

C

Statement-1 is True, Statement-2 is False

D

Statement-1 is False, Statement-2 is true

Text Solution

AI Generated Solution

The correct Answer is:
To solve the problem, we need to analyze the two statements regarding the planes \( P_1 \) and \( P_2 \) and the lines \( L_1 \) and \( L_2 \) contained within them. ### Step 1: Understanding the Relationship Between Planes and Lines We are given two planes \( P_1 \) and \( P_2 \) that are parallel. By definition, if two planes are parallel, they do not intersect. **Hint:** Remember that parallel planes have the same normal vector and do not meet at any point. ### Step 2: Analyzing Statement 1 **Statement 1:** If \( P_1 \) and \( P_2 \) are parallel, then \( L_1 \) and \( L_2 \) must be parallel. This statement is **false**. While the planes are parallel, the lines contained in them can be oriented in different directions. For instance, \( L_1 \) could be slanted in one direction while \( L_2 \) could be slanted in another direction, leading to them being skew lines (not parallel and not intersecting). **Hint:** Consider the possibility of skew lines existing in parallel planes. ### Step 3: Analyzing Statement 2 **Statement 2:** If \( P_1 \) and \( P_2 \) are parallel, then \( L_1 \) and \( L_2 \) may not have a common point. This statement is **true**. Since the planes do not intersect, the lines contained within them can either be parallel (and thus do not intersect) or skew (not parallel and also do not intersect). In both cases, they do not have a common point. **Hint:** Think about the definitions of parallel and skew lines and how they relate to the planes. ### Conclusion - **Statement 1** is **false**: \( L_1 \) and \( L_2 \) do not have to be parallel even if \( P_1 \) and \( P_2 \) are parallel. - **Statement 2** is **true**: \( L_1 \) and \( L_2 \) may not have a common point when \( P_1 \) and \( P_2 \) are parallel. **Final Answer:** - Statement 1: False - Statement 2: True
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