(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 $\vec{a}, \vec{b}, \vec{c}$ are linearly dependent because there exist scalars $x, y, z$ (not all zero) such that $x\vec{a} + y\vec{b} + z\vec{c} = \vec{0}$. Thus,statement $II$ is true.$\therefore$ Both $I$ and $II$ are true.

Class 11 Chemistry Data Entry - Chemistry Level 0 of all question bank

$I$. 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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For the reaction $SnO_{2(s)} + 2H_{2(g)} \rightleftharpoons 2H_2O_{(g)} + Sn_{(l)}$,calculate $K_p$ at $900 \, K$,where the equilibrium steam-hydrogen mixture was $45 \% \, H_2$ by volume.

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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?