The vectors 3a-2b-4c, -a+2c, -2a+b+3c are

linearly dependent

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linearly independent

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collinear

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none

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Solution

The correct option is A linearly dependent
$B o x = ∣ ∣ ∣ ∣ \begin{matrix} 3 & - 2 & - 4 - 1 & 0 & 2 - 2 & 1 & 3 \end{matrix} ∣ ∣ ∣ ∣ = 3 (0 - 2) + 2 (- 3 + 4) - 4 (- 1 - 0) = - 6 + 2 + 4 = 0$
$∴$ Given vectors are coplanar Given vectors are linarly dependent.

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¯ ¯ ¯ a, ¯ ¯ b, ¯ ¯ c

3 ¯ ¯ ¯ a - 2 ¯ ¯ b - 4 ¯ ¯ c

- ¯ ¯ ¯ a + 2 ¯ ¯ c

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\to a, \to b, \to c

{∣ ∣ ∣ 2 \to a - 3 \to b ∣ ∣ ∣}^{2} + {∣ ∣ ∣ 2 \to b - 3 \to c ∣ ∣ ∣}^{2} + {∣ ∣ 2 \to c - 3 \to a ∣ ∣}^{2}

¯ a, ¯ b, ¯ c

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