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Consider the following
Let Q be the image o f the point P ( - 2 , 1, - 5 ) in the plane 3x-2y+2z+ 1=0.
1. The coordinates of Q are (4, -3, -1).
2. PQ is of length more than 8 units.
3. The point (1, -1, -3) is the mid-point of the line segment PQ and lies on the given plane.
Q. Which of the above statements are correct?
  • a)
    1 and 2 only
  • b)
    2 and 3 only
  • c)
    1 and 3 only
  • d)
    1,2 and 3
Correct answer is option 'D'. Can you explain this answer?
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Consider the followingLet Q be the image o f the point P ( - 2 , 1, - ...
Given Statements:
1. The coordinates of Q are (4, -3, -1).
2. PQ is of length more than 8 units.
3. The point (1, -1, -3) is the mid-point of the line segment PQ and lies on the given plane.

Explanation:

Statement 1:
- To find the image Q of point P in the given plane, we can use the formula for the image of a point in a plane.
- Given point P(-2, 1, -5) and the plane 3x-2y+2z+1=0, we can substitute the coordinates of P in the formula to find Q.
- By substituting (-2, 1, -5) in the equation of the plane, we find that Q has coordinates (4, -3, -1).
- Therefore, statement 1 is correct.

Statement 2:
- The length of PQ can be found using the distance formula in 3D space.
- The distance between points P(-2, 1, -5) and Q(4, -3, -1) is calculated to be more than 8 units.
- Hence, statement 2 is correct.

Statement 3:
- Given that the point (1, -1, -3) is the mid-point of the line segment PQ and lies on the given plane.
- Since the midpoint of PQ is (1, -1, -3) and Q is (4, -3, -1), the coordinates satisfy the condition.
- Therefore, statement 3 is correct.

Conclusion:
- All three statements are correct as explained above. So, the correct answer is option 'D'.
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Consider the followingLet Q be the image o f the point P ( - 2 , 1, - 5 ) in the plane 3x-2y+2z+ 1=0.1. The coordinates of Q are (4, -3, -1).2. PQ is of length more than 8 units.3. The point (1, -1, -3) is the mid-point of the line segment PQ and lies on the given plane.Q. Which of the above statements are correct?a)1 and 2 onlyb)2 and 3 onlyc)1 and 3 onlyd)1,2 and 3Correct answer is option 'D'. Can you explain this answer?
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Consider the followingLet Q be the image o f the point P ( - 2 , 1, - 5 ) in the plane 3x-2y+2z+ 1=0.1. The coordinates of Q are (4, -3, -1).2. PQ is of length more than 8 units.3. The point (1, -1, -3) is the mid-point of the line segment PQ and lies on the given plane.Q. Which of the above statements are correct?a)1 and 2 onlyb)2 and 3 onlyc)1 and 3 onlyd)1,2 and 3Correct answer is option 'D'. Can you explain this answer? for Defence 2024 is part of Defence preparation. The Question and answers have been prepared according to the Defence exam syllabus. Information about Consider the followingLet Q be the image o f the point P ( - 2 , 1, - 5 ) in the plane 3x-2y+2z+ 1=0.1. The coordinates of Q are (4, -3, -1).2. PQ is of length more than 8 units.3. The point (1, -1, -3) is the mid-point of the line segment PQ and lies on the given plane.Q. Which of the above statements are correct?a)1 and 2 onlyb)2 and 3 onlyc)1 and 3 onlyd)1,2 and 3Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Defence 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider the followingLet Q be the image o f the point P ( - 2 , 1, - 5 ) in the plane 3x-2y+2z+ 1=0.1. The coordinates of Q are (4, -3, -1).2. PQ is of length more than 8 units.3. The point (1, -1, -3) is the mid-point of the line segment PQ and lies on the given plane.Q. Which of the above statements are correct?a)1 and 2 onlyb)2 and 3 onlyc)1 and 3 onlyd)1,2 and 3Correct answer is option 'D'. Can you explain this answer?.
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