Plane parallel to two given directions (normal = cross product) through a given point
This type of question, asked 5 times: 2021 Paper 10, 25 Jun 2022, 28 Jul 2022, 30 Jan 2023, 13 Apr 2023. All 5 questions below, oldest first.
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Question 1
2021 Paper 10
89
Let P be a plane containing the line 3x−1=4y+6=2z+5 and parallel to the line 4x−3=−3y−2=7z+5. If the point (1,−1,α) lies on the plane P, then the value of ∣5α∣ is equal to
Question 2
25 Jun 2022
88
Let the lines
L1:r=λ(i+2j+3k),λ∈R
L2:r=(i+3j+k)+μ(i+j+5k);μ∈R
intersect at the point S. If a plane ax+by−z+d=0 passes through S and is parallel to both the lines L1 and L2, then the value of a+b+d is equal to
Question 3
28 Jul 2022
166
A plane P is parallel to two lines whose direction ratios are −2,1,−3, and −1,2,−2 and it contains the point (2,2,−2). Let P intersect the co-ordinate axes at the points A,B,C making the intercepts α,β,γ. If V is the volume of the tetrahedron OABC, where O is the origin and p=α+β+γ, then the ordered pair (V,p) is equal to
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Question 4
30 Jan 2023
165
If a plane passes through the points (−1,k,0),(2,k,−1),(1,1,2) and is parallel to the line 1x−1=22y+1=−1z+1, then the value of (k−1)(k−2)k2+1 is
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Question 5
13 Apr 2023
153
The plane, passing through the points (0,−1,2) and (−1,2,1) and parallel to the line passing through (5, 1,−7) and (1,−1,−1), also passes through the point.
