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

Find the odd one out of the following

(a)

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

(b)

\(2\hat { i } +4\hat { j } +6\hat { k } \)

(c)

\(7\hat { i } +14\hat { j } +21\hat { k } \)

(d)

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

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

Find the odd one out of the following

(a)

matrix multiplication

(b)

vector cross product

(c)

Subtraction

(d)

Matrix Addition