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If the points whose position vectors are $2 i + j + k, 6 i - j + 2 k$ and $14 i - 5 j + p k$ are collinear, then the value of p is

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answer is B.

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Detailed Solution

AB=OB-OA=4i-2j+k , AC=OC-OA=12i-6j+(p-1)k

A,B,C are collinear $\vec{A C} = λ \vec{A B} \Rightarrow 12 i$

6j+(p-1)k= $λ$ (4i-2j+k)

$\Rightarrow λ = 3, p - 1 = 3 \Rightarrow p = 4$

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