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A line passes through A(4, –6, –2) and B(16, –2,4). The point P(a, b, c) where a, b, c are non-negative integers, on the line AB lies at a distance of 21 units, from the point A. The distance between the points P(a, b, c) and Q(4,  –12, 3) is equal to ____. 
  • a)
    •  
  • b)
    ERROR
  • c)
    ERROR
  • d)
    ERROR
Correct answer is '22'. Can you explain this answer?
Most Upvoted Answer
A line passes through A(4, –6, –2) and B(16, –2,4). ...
Understanding the Problem
To solve the problem, we first need to find the line passing through points A(4, –6, –2) and B(16, –2, 4). We will then find point P that is 21 units away from A and lies on this line.
Finding the Direction Vector
- The direction vector AB can be found as follows:
- AB = B - A = (16 - 4, -2 + 6, 4 + 2) = (12, 4, 6)
Parametric Equations of the Line
- The line can be represented parametrically as:
- x = 4 + 12t
- y = -6 + 4t
- z = -2 + 6t
Finding Point P
- We need the distance from A to P to be 21 units:
- Distance formula: d = √[(x - x1)² + (y - y1)² + (z - z1)²]
- Setting this to 21 units:
- √[(12t)² + (4t)² + (6t)²] = 21
- This simplifies to: 14t = 21 → t = 21/14 = 3/2
Coordinates of Point P
- Substituting t = 3/2 into the parametric equations:
- x = 4 + 12(3/2) = 22
- y = -6 + 4(3/2) = 0
- z = -2 + 6(3/2) = 7
Thus, P(22, 0, 7).
Calculating Distance from P to Q
- Now, we calculate the distance between P(22, 0, 7) and Q(4, –12, 3):
- Distance = √[(22 - 4)² + (0 + 12)² + (7 - 3)²]
- This results in = √[(18)² + (12)² + (4)²] = √(324 + 144 + 16) = √484 = 22.
Final Answer
- Therefore, the distance between points P and Q is 22 units.
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A line passes through A(4, –6, –2) and B(16, –2,4). ...
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A line passes through A(4, –6, –2) and B(16, –2,4). The point P(a, b, c) where a, b, c are non-negative integers, on the line AB lies at a distance of 21 units, from the point A. The distance between the points P(a, b, c) and Q(4, –12, 3) is equal to ____.a) b)ERRORc)ERRORd)ERRORCorrect answer is '22'. Can you explain this answer?
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A line passes through A(4, –6, –2) and B(16, –2,4). The point P(a, b, c) where a, b, c are non-negative integers, on the line AB lies at a distance of 21 units, from the point A. The distance between the points P(a, b, c) and Q(4, –12, 3) is equal to ____.a) b)ERRORc)ERRORd)ERRORCorrect answer is '22'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A line passes through A(4, –6, –2) and B(16, –2,4). The point P(a, b, c) where a, b, c are non-negative integers, on the line AB lies at a distance of 21 units, from the point A. The distance between the points P(a, b, c) and Q(4, –12, 3) is equal to ____.a) b)ERRORc)ERRORd)ERRORCorrect answer is '22'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A line passes through A(4, –6, –2) and B(16, –2,4). The point P(a, b, c) where a, b, c are non-negative integers, on the line AB lies at a distance of 21 units, from the point A. The distance between the points P(a, b, c) and Q(4, –12, 3) is equal to ____.a) b)ERRORc)ERRORd)ERRORCorrect answer is '22'. Can you explain this answer?.
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