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Collinear Vectors

If the points...

Question

If the points A,B and C have position vectors (2,1,1), (6,-1,2) and (14,-5,P) respectively and if they are collinear, then P =

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Solution

The correct option is B
4

$\to O A = 2^i +^j +^k, \to O B = 6^i -^j + 2^k, \to O C = 14^i - 5^j + P^k \Rightarrow \to A B = \to O B - \to O A = 4^i - 2^j +^k, \to A C = \to O C - \to O A = 12^i - 6^j + (p - 1)^k$
A, B, C are collinear $\Rightarrow \to A C = λ \to A B \Rightarrow 12^i - 6^j + (p - 1)^k = λ (4^i - 2^j +^k)$
$\Rightarrow λ = 3, p - 1 = 3 \Rightarrow p = 4.$

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