The vectors 3a-2b-4c, -a+2c, -2a+b+3c are Options: A . &nbsplinearly dependent B . &nbsplinearly independent C . &nbspcollinear D . &nbspnone

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

Question

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

Options:

A . linearly dependent

B . linearly independent

C . collinear

D . none

Answer: Option A
:
A

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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