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Line x is a line parallel to the x-axis. Lines p and q are at angle 70° and 60° respectively w.r.t line x. If p and q are rotated clockwise by a° and b° respectively, such that a = b + 10, what is the magnitude of the minimum possible angle between lines p and q?
  • a)
    10°
  • b)
  • c)
    20°
  • d)
    Cannot be determined
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
Line x is a line parallel to the x-axis. Lines p and q are at angle 70...
Since the orientation of the two lines (i.e. clockwise or anti-clockwise) is not given, consider each case.
Assume that lines p and q are both anti-clockwise w.r.t the x-axis, When they are rotated at a° and (a - 10)° clockwise, their final orientation w.r.t the x-axis becomes:
Line p: (70 - a)° Line q: [60 - (a - 10)]° i.e. (70 - a)° In this case, the lines p and q are parallel and the magnitude of the angle between them is 0.
Since the magnitude of the minimum angle is required, this value cannot be less than 0.
Since the minimum angle has been established as 0° in this case, there is no need to check any other case.
Hence, option 2.
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Most Upvoted Answer
Line x is a line parallel to the x-axis. Lines p and q are at angle 70...
To find the magnitude of the minimum possible angle between lines p and q, we need to consider the rotation of each line and their respective angles with respect to the x-axis.

Let's analyze the given information step by step:

1. Line x is parallel to the x-axis:
- This means that line x is horizontal and has an angle of 0 degrees with respect to the x-axis.

2. Lines p and q are at angles 70 and 60 degrees respectively with respect to line x:
- Line p makes an angle of 70 degrees with line x.
- Line q makes an angle of 60 degrees with line x.

3. Lines p and q are rotated clockwise by a and b degrees respectively, with a = b + 10:
- After rotation, line p makes an angle of 70 + a degrees with line x.
- After rotation, line q makes an angle of 60 + b degrees with line x.

4. To find the minimum possible angle between lines p and q, we need to minimize the difference between their angles:
- Let's assume that the difference between the angles after rotation is d degrees.
- So, the angle between lines p and q becomes (70 + a) - (60 + b) = 10 + d degrees.

Now, since a = b + 10, we can substitute the value of a in terms of b in the above equation:
- (70 + b + 10) - (60 + b) = 10 + d
- 80 - 60 = 10 + d
- 20 = 10 + d
- d = 10

Therefore, the minimum possible angle between lines p and q is 10 degrees. Hence, the correct answer is option (B).
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Line x is a line parallel to the x-axis. Lines p and q are at angle 70° and 60° respectively w.r.t line x. If p and q are rotated clockwise by a° and b° respectively, such that a = b + 10, what is the magnitude of the minimum possible angle between lines p and q?a)10°b)0°c)20°d)Cannot be determinedCorrect answer is option 'B'. Can you explain this answer?
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