(C) $I$: Two vectors $\vec{a}$ and $\vec{b}$ are linearly independent if and only if they are non-zero and non-collinear. Thus, statement $I$ is true.

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(C) $I$: Two vectors $\vec{a}$ and $\vec{b}$ are linearly independent if and only if they are non-zero and non-collinear. Thus, statement $I$ is true.$II$: Any three coplanar vectors in a $3D$ space are linearly dependent because one can be expressed as a linear combination of the other two if they are not collinear, or they are linearly dependent if any two are collinear. Thus, statement $II$ is true.$\therefore$ Both $I$ and $II$ are true.

Class 12 Mathematics Vector Algebra Basic , Modulus and Algebra of vectors

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$I$. Two non-zero, non-collinear vectors are linearly independent.
$II$. Any three coplanar vectors are linearly dependent.
Which of the above statements is/are true?

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A
Only $I$
B
Only $II$
C
Both $I$ and $II$
D
Neither $I$ nor $II$

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$I$. Two non-zero, non-collinear vectors are linearly independent.$II$. Any three coplanar vectors are linearly dependent.Which of the above statements is/are true?

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$I$. Two non-zero, non-collinear vectors are linearly independent.
$II$. Any three coplanar vectors are linearly dependent.
Which of the above statements is/are true?