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Let Q be the mirror image of the point P(1, 0, 1) with respect to the plane S: x + y + z = 5. If a line L passing through (1, -1, -1), parallel to the line PQ meets the plane S at R, then QR2 is equal to:
- a)2
- b)5
- c)7
- d)11
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
Let Q be the mirror image of the point P(1, 0, 1) with respect to the ...
Let parallel vector of L =
mirror image of Q on given plane x + y + z = 5
a = 3, b = 2, c = 3
Q ≡ (3, 2, 3)
so,
= (1, 1, 1)Equation of line
Let point R, (λ + 1,λ – 1, λ – 1) lying on plane x + y + z = 5,
so 3λ – 1 = 5
⇒ λ = 2
Point R is (3, 1, 1)
QR2 = 5
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Community Answer
Let Q be the mirror image of the point P(1, 0, 1) with respect to the ...
Explanation:
1. Finding the Mirror Image Q:
- The mirror image of a point P with respect to a plane can be found by reflecting the point across the plane. Given P(1, 0, 1) and the plane equation x + y + z = 5, we can find the mirror image Q by using the formula for the reflection of a point across a plane.
2. Finding the Line L:
- The line passing through (1, -1, -1) parallel to the line PQ can be determined by finding the direction vector of PQ and using it to form the equation of the line passing through (1, -1, -1).
3. Calculating Point of Intersection R:
- Since the line L is parallel to PQ, it will have the same direction vector. Using this information, we can find the point of intersection R of the line L with the plane S by substituting the equation of the line into the plane equation.
4. Calculating QR:
- Once we have the coordinates of Q and R, we can calculate the distance QR using the distance formula in three dimensions: QR = sqrt((x2 - x1)^2 + (y2 - y1)^2 + (z2 - z1)^2).
5. Calculating QR^2:
- After finding QR, we can find QR^2 by squaring the distance QR calculated in the previous step.
Therefore, the correct answer is option 'B' (5), which is the value of QR^2.
1. Finding the Mirror Image Q:
- The mirror image of a point P with respect to a plane can be found by reflecting the point across the plane. Given P(1, 0, 1) and the plane equation x + y + z = 5, we can find the mirror image Q by using the formula for the reflection of a point across a plane.
2. Finding the Line L:
- The line passing through (1, -1, -1) parallel to the line PQ can be determined by finding the direction vector of PQ and using it to form the equation of the line passing through (1, -1, -1).
3. Calculating Point of Intersection R:
- Since the line L is parallel to PQ, it will have the same direction vector. Using this information, we can find the point of intersection R of the line L with the plane S by substituting the equation of the line into the plane equation.
4. Calculating QR:
- Once we have the coordinates of Q and R, we can calculate the distance QR using the distance formula in three dimensions: QR = sqrt((x2 - x1)^2 + (y2 - y1)^2 + (z2 - z1)^2).
5. Calculating QR^2:
- After finding QR, we can find QR^2 by squaring the distance QR calculated in the previous step.
Therefore, the correct answer is option 'B' (5), which is the value of QR^2.
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Let Q be the mirror image of the point P(1, 0, 1) with respect to the plane S: x + y + z = 5. If a line L passing through (1, -1, -1), parallel to the line PQ meets the plane S at R, then QR2is equal to:a)2b)5c)7d)11Correct answer is option 'B'. Can you explain this answer?
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Let Q be the mirror image of the point P(1, 0, 1) with respect to the plane S: x + y + z = 5. If a line L passing through (1, -1, -1), parallel to the line PQ meets the plane S at R, then QR2is equal to:a)2b)5c)7d)11Correct answer is option 'B'. 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 Let Q be the mirror image of the point P(1, 0, 1) with respect to the plane S: x + y + z = 5. If a line L passing through (1, -1, -1), parallel to the line PQ meets the plane S at R, then QR2is equal to:a)2b)5c)7d)11Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let Q be the mirror image of the point P(1, 0, 1) with respect to the plane S: x + y + z = 5. If a line L passing through (1, -1, -1), parallel to the line PQ meets the plane S at R, then QR2is equal to:a)2b)5c)7d)11Correct answer is option 'B'. Can you explain this answer?.
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