Assertion (A) : \(\overset { \rightarrow }{ a } ,\overset { \rightarrow }{ b } ,\overset { \rightarrow }{ c } \) are the position vector three collinear points then 2 \(\overset { \rightarrow }{ a }=\overset { \rightarrow }{ b } +\overset { \rightarrow }{ c } \)
Reason (R): Collinear points, have same direction

Assertion (A): If ABCD is a parallelogram, \(\overset { \rightarrow }{ AB } +\overset { \rightarrow }{ AD } +\overset { \rightarrow }{ CB } +\overset { \rightarrow }{ CD } \) then is equal zero.
Reason (R): \(\overset { \rightarrow }{ AB } \) and \(\overset { \rightarrow }{ CD } \) are equal in magnitude and opposite in direction. Also\( \overset { \rightarrow }{ AD } \) and \( \overset { \rightarrow }{ CB } \) are equal in magnitude and opposite in direction

If m \(\left( \overset { \rightarrow }{ 2 } +\overset { \rightarrow }{ j } +\overset { \rightarrow }{ k } \right) \) is a unit vector then the value of m is ___________ .

The angle between two vectors \(\vec{a}\) and \(\vec{b}\) with magnitudes\(\sqrt{3}\) and 4 respectively and \(\vec{a}.\vec{b}=2\sqrt{3}\) is ________ .

The vector in the direction of the vector\(\hat{i}-2\hat{j}+2\hat{k}\) that has magnitude 9 is _________ .

The vectors from origin to the points A and B are \(2\hat { i } -3\hat { j } +2\hat { k } \) and \(2\hat { i } +3\hat { j } +\hat { k } \) respectively, then the area of \(\Delta\)OAB is equal to

If \(\overrightarrow{a}=\hat{i}+2\hat{j}+2\hat{k},|\overrightarrow{b}|=5\) and the angle between \(\overrightarrow{a}\) and \(\overrightarrow{b}\) is \({\pi\over 6},\) then the area of the triangle formed by these two vectors as two sides, is

The vectors \(\overrightarrow{a}-\overrightarrow{b},\overrightarrow{b}-\overrightarrow{c},\overrightarrow{c}-\overrightarrow{a}\) are

The unit vector parallel to the resultant of the vectors \(\hat{i}+\hat{j}-\hat{k}\) and \(\hat{i}-2\hat{j}+\hat{k}\) is

The value of \(\overrightarrow{AB}+\overrightarrow{BC}+\overrightarrow{DA}+\overrightarrow{CD}\) is