Test for Collinearity of Points

Q. If the position vectors of three points are $\overrightarrow{a}-2\overrightarrow{b}+3\overrightarrow{c},2\overrightarrow{a}+3\overrightarrow{b}+4\overrightarrow{c},-7\overrightarrow{b}+10\overrightarrow{c}$, then the three points are

1. collinear
2. non – coplanar
3. non – collinear
4. None of these

Q. If $\overrightarrow{AO}+\overrightarrow{OB}=\overrightarrow{BO}+\overrightarrow{OC}$, then

1. A, B and C are collinear
2. A, B and C are not collinear
3. Nothing can be said about Collinearity from this information
4. $\overrightarrow{A},\overrightarrow{B},\overrightarrow{C}$ form a triangle

Q. If $\overrightarrow{A}=(\overrightarrow{a}-2\overrightarrow{b}+3\overrightarrow{c})$
$\overrightarrow{B}=(-2\overrightarrow{a}+3\overrightarrow{b}+2\overrightarrow{c})$
$\overrightarrow{C}=(-8\overrightarrow{a}+13\overrightarrow{b})$
Then $\overrightarrow{AB}$ and $\overrightarrow{AC}$ are collinear

1. True
2. False