Fundamental Theorem in 2D

Q. Any vector $\overrightarrow{r}$ in the plane of two non-zero, non collinear vectors $\overrightarrow{a}$ and $\overrightarrow{b}$ can be expressed uniquely as a linear combination $x\overrightarrow{a}+y\overrightarrow{b}$ of $\overrightarrow{a}and\overrightarrow{b},$ where $x\overrightarrow{a}andy\overrightarrow{b}$ are the components of vector $\overrightarrow{r}$

1. True
2. False

Q. Find the value of $k_1$ and $k_2$ for which $\overrightarrow{V}$ can be represented as $\overrightarrow{V}=k_1\overrightarrow{A}+k_2\overrightarrow{B}$. Where, $\overrightarrow{V}=2i-j$ ,
$\overrightarrow{A}=3i-2j$ and $\overrightarrow{B}=3i+3j.$

1. $k_1=1$ and $k_2=1$
2. $k_1=\frac{3}{5}\text{and}{k}_2=\frac{1}{2}$
3. $k_1=\frac{3}{5}\text{and}{k}_2=\frac{1}{15}$
4. $k_1=\frac{-2}{3}\text{and}{k}_2=\frac{2}{5}$

Q. Which of the following statements is / are true?
1.Set of two vectors $\overrightarrow{a},\overrightarrow{b}$ is linearly dependent if and only if either any of $\overrightarrow{a}\text{and}\overrightarrow{b}$ is zero or they are parallel
2.$\overrightarrow{a},\overrightarrow{b}\text{and}\overrightarrow{c}$ are linearly dependent $\iff \overrightarrow{a},\overrightarrow{b}\text{and}\overrightarrow{c}$ are coplanar.

1. Both $1$ and $2$ are false
2. $1$ is true and $2$ is false
3. Both $1$ and $2$ are true
4. $2$ is true and $1$ is false