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Question

If the points (1,3,2),(4,2,2) and (5,5,λ) are collinear, then λ is equal to

A
10
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B
5
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C
5
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D
10
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Solution

The correct option is D 10
Let the points be A(1,3,2)B(4,2,2)C(5,5,λ)
Direction ratio of AB=(3,1,4)
If A,B,C are collinear points then direction ratio of AB and BC must be proportional.
Direction ratio of BC=(9,3,λ+2)
9=α(3)
3=α(1)
λ+2=α(4) and α=3
λ+23=4
λ=10

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