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Equation of Plane Passing through Three Points

If the points...

Question

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?

A

2

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B

4

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C

6

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D

8

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Solution

The correct option is B $4$
$P o s i t i v e v e c t o r a r e 2 i + j + k, 6^i +^j + 2^k a n d 4 i - 5 j + p k a r e c o l l i n e a r t h e n P = 2 i f t h r e e p o s i t i o n v e c t o r s a r e c o l l i n e a r t h e n, i t s d e t e r m i n a n t s i s (0) \Rightarrow ∣ ∣ ∣ ∣ \begin{matrix} 211 6 - 12 14 - 5 P \end{matrix} ∣ ∣ ∣ ∣ = 0 \Rightarrow 2 (- P + 10) - 1 (6 P - 28) + (- 30 + 14) = 0 \Rightarrow - 2 P + 20 - 6 P + 28 - 16 = 0 \Rightarrow - 8 P + 32 = 0 ∴ P = 4$

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