If ⃗a=2^i+3^j+^k,⃗b=2^i+p^j+3^k and ⃗c=2^i+17^j+3^k are c

Question -

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

Options:

A . -4

B . -1

C . 4

D . -2

Answer: Option A
:
A
Since,

⃗ a = 2^i + 3^j +^k, ⃗ b = 2^i + p^j + 3^k

and

⃗ c = 2^i + 17^j + 3^k

are coplanar,
therefore

[⃗ a ⃗ b ⃗ c] = ∣ ∣∣ ∣ \begin{matrix} 2 & 3 & 1 2 & p & 3 2 & 17 & - 3 \end{matrix} ∣ ∣∣ ∣ = 0 \Rightarrow p = - 4

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