Triangle formed by a point, its foot or image in a line and another point: its area
This type of question, asked 5 times: 31 Jan 2023, 6 Apr 2024, 23 Jan 2025, 24 Jan 2025, 6 Apr 2026 S2. All 5 questions below, oldest first.
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Question 1
31 Jan 2023
88
Let the line L:2x−1=−1y+1=1z−3 intersect the plane 2x+y+3z=16 at the point P. Let the point Q be the foot of perpendicular from the point R(1,−1,−3) on the line L. If α is the area of triangle PQR, then α2 is equal to
Question 2
6 Apr 2024
164
Let P(α,β,γ) be the image of the point Q(3,−3,1) in the line 1x−0=1y−3=−1z−1 and R be the point (2,5,−1). If the area of the triangle PQR is λ and λ2=14K, then K is equal to:
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Question 3
23 Jan 2025
59
Let P be the foot of the perpendicular from the point Q(10,−3,−1) on the line 7x−3=−1y−2=−2z+1. Then the area of the right angled triangle PQR, where R is the point (3,−2,1), is
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Question 4
24 Jan 2025
147
Let P be the image of the point Q(7,−2,5) in the line L:2x−1=3y+1=4z and R(5,p,q) be a point on L. Then the square of the area of △PQR is
Question 5
6 Apr 2026 S2
74
Let the image of the point P(0,−5,0) in the line 2x−1=1y=−2z+1 be the point R and the image of the point Q(0,2−1,0) in the line −1x−1=4y+9=1z+1 be the point S. Then the square of the area of the parallelogram PQRS is ____ .
