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Question
If the line passes through the points P(6,−1,2),Q(8,−7,2λ) and R(5,2,4) then value of λ is ________.
If the line passes through the points P(6,−1,2),Q(8,−7,2λ) and R(5,2,4) then value of λ is ________.
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Solution
The correct option is B −1
If a single line passes through the three points P, Q and R, then, Q is of the form t.P+(1−t).R, for some t∈R.So we have, 8=6t+5(1−t),−7=−t+2(1−t) and 2λ=2t+4(1−t).The first of these equations gives us t=3.Substituting t=3 in the last equation, we getλ=−1.
If a single line passes through the three points P, Q and R, then, Q is of the form t.P+(1−t).R, for some t∈R.
So we have,
8=6t+5(1−t),−7=−t+2(1−t) and 2λ=2t+4(1−t).
The first of these equations gives us t=3.
Substituting t=3 in the last equation, we get
λ=−1.
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