Test for Collinearity of Points

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

1. True
2. False

Q. The vectors $2\hat{i}+3\hat{j},5\hat{i}+6\hat{j}$ and $8\hat{i}+\alpha \hat{j}$ have their initial points at $(1,1)$. The value of $\alpha$ so that the vectors terminate on one straight line is

1. $9$
2. $3$
3. $6$
4. $0$

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

Q. The points A, B and C with position vectors $-2\hat{i}+3\hat{j}+5\hat{k},\hat{i}+2\hat{j}+3\hat{k}and7\hat{i}-\hat{k}$ respectively are non collinear.

1. True
2. False