Four points with given position vectors or coordinates are coplanar: find the unknown
This type of question, asked 4 times: 2021 Paper 25, 29 Jul 2022, 25 Jan 2023, 6 Apr 2023. All 5 questions below, oldest first.
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Question 1
2021 Paper 25
78
If (1,5,35),(7,5,5),(1,λ,7) and (2λ,1,2) are coplanar, then the sum of all possible values of λ is:
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Question 2
29 Jul 2022
165
If (2,3,9),(5,2,1),(1,λ,8) and (λ,2,3) are coplanar, then the product of all possible values of λ is:
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Question 3
25 Jan 2023
152
If the four points, whose position vectors are 3i−4j+2k,i+2j−k,−2i−j+3k and 5i−2αj+4k are coplanar, then α is equal to
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Question 4
6 Apr 2023
157
The sum of all values of α, for which the points whose position vectors i−2j+3k,2i−3j+4k, (α+1)i+2k and 9i+(α−8)j+6k are coplanar, is equal to
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Question 5
6 Apr 2023
79
Let the position vectors of the points A,B,C and D be 5i+5j+2λk,i+2j+3k,−2i+λj+4k and −i+5j+6k. Let S={λ∈R: the points A,B,C and D are coplanar}. Then ∑λ∈S(λ+2)2 is equal to
