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

(a)

\(\overrightarrow{AD}\)

(b)

\(\overrightarrow{CA}\)

(c)

\(\overrightarrow{0}\)

(d)

\(-\overrightarrow{AD}\)

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

(a)

\({\hat{i}-\hat{j}+\hat{k}\over\sqrt{5}}\)

(b)

\({2\hat{i}+\hat{j}\over\sqrt{5}}\)

(c)

\({2\hat{i}-\hat{j}+\hat{k}\over\sqrt{5}}\)

(d)

\({2\hat{i}-\hat{j}\over\sqrt{5}}\)

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

(a)

parallel to each other

(b)

unit vectors

(c)

mutually perpendicular vectors

(d)

coplanar vectors.

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

(a)

\(7\over4\)

(b)

\(15\over4\)

(c)

\(3\over4\)

(d)

\(17\over4\)

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

(a)

340

(b)

5

(c)

\(\sqrt { 229 } \)

(d)

\(\frac { 1 }{ 2 } \sqrt { 229 } \)

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

(a)

\(\hat{i}-2\hat{j}+2\hat{k}\)

(b)

\(\frac { \hat { i } -2\hat { j } +2\hat { k } }{ 3 } \)

(c)

3(\(\hat{i}-2\hat{j}+2\hat{k}\))

(d)

9(\(\hat{i}-2\hat{j}+2\hat{k}\))

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 ________ .

(a)

\(\frac{\pi}{6}\)

(b)

\(\frac { \pi }{ 3 } \)

(c)

\(\frac { \pi }{ 2 } \)

(d)

\(\frac { 5\pi }{ 2 } \)

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

(a)

\(\pm \frac { 1 }{ \sqrt { 3 } } \)

(b)

\(\pm \frac { 1 }{ \sqrt { 5 } } \)

(c)

\(\pm \frac { 1 }{ \sqrt { 6 } } \)

(d)

\(\pm \frac { 1 }{ {2 } } \)

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

(a)

Both A and R are true and R is the correct explanation of A

(b)

Both A and R are true and R is not a correct explantion of A

(c)

A is true but R is false

(d)

A is false but R is true

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

(a)

Both A and R are true and R is the correct explanation of A

(b)

Both A and R are true and R is not a correct explantion of A

(c)

A is true but R is false

(d)

A is false but R is true