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Test for Coplanarity

If a⃗=2 î+3 ĵ...

Question

If $\to a = 2^i + 3^j +^k, \to b = 2^i + p^j + 3^k$ and $\to c = 2^i + 17^j + 3^k$ are coplanar vectors, then the value of p is

A

-4

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B

-1

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C

4

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D

-2

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Solution

The correct option is A -4
Since, $\to a = 2^i + 3^j +^k, \to b = 2^i + p^j + 3^k$ and $\to c = 2^i + 17^j + 3^k$ are coplanar,
therefore $[\to a \to b \to c] = ∣ ∣ ∣ ∣ \begin{matrix} 2 & 3 & 1 2 & p & 3 2 & 17 & - 3 \end{matrix} ∣ ∣ ∣ ∣ = 0 \Rightarrow p = - 4$

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