If \(\overrightarrow{a}+2\overrightarrow{b}\) and \(3\overrightarrow{a}+m\overrightarrow{b}\) are parallel, then the value of m is

(a)

3

(b)

\(1\over3\)

(c)

6

(d)

\(1\over6\)

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)

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

A vector \(\overrightarrow{OP}\) makes 60° and 45° with the positive direction of the x and y axes respectively.  Then the angle between \(\overrightarrow{OP}\)and the z-axis is

(a)

45°

(b)

60°

(c)

90°

(d)

30°

If \(\overrightarrow{BA}=3\hat{i}+2\hat{j}+\hat{k}\) and the position vector of B is \(\hat{i}+3\hat{j}-\hat{k}\) ,then the position vector of A is

(a)

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

(b)

\(4\hat{i}+5\hat{j}\)

(c)

\(4\hat{i}\)

(d)

\(-4\hat{i}\)

A vector makes equal angle with the positive direction of the coordinate axes. Then each angle is equal to

(a)

\(cos^{-1}({1\over 3})\)

(b)

\(cos^{-1}({2\over 3})\)

(c)

\(cos^{-1}({1\over\sqrt 3})\)

(d)

\(cos^{-1}({2\over\sqrt 3})\)

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 ABCD is a parallelogram, then \(\overrightarrow{AB}+\overrightarrow{AD}+\overrightarrow{CB}+\overrightarrow{CD}\) is equal to

(a)

\(2(\overrightarrow{AB}+\overrightarrow{AD})\)

(b)

\(4\overrightarrow{AC}\)

(c)

\(4\overrightarrow{BD}\)

(d)

\(\overrightarrow{0}\)

One of the diagonals of parallelogram ABCD with \(\overrightarrow{a}\) and \(\overrightarrow{b}\) as adjacent sides is \(\overrightarrow{a}+\overrightarrow{b}\) The other diagonal \(\overrightarrow{BD}\) is

(a)

\(\overrightarrow{a}-\overrightarrow{b}\)

(b)

\(\overrightarrow{b}-\overrightarrow{a}\)

(c)

\(\overrightarrow{a}+\overrightarrow{b}\)

(d)

\(\overrightarrow{a}+\overrightarrow{b}\over 2\)

If \(\overrightarrow{r}={9\overrightarrow{a}+7\overrightarrow{b}\over16}\), then the point P whose position vector \(\overrightarrow{r}\) divides the line joining the points with position vectors \(\overrightarrow{a}\) and \(\overrightarrow{b}\) in the ratio

(a)

7: 9 internally

(b)

9: 7 internally

(c)

9: 7 externally

(d)

7: 9 externally

If \(\overrightarrow{a}\)  and \(\overrightarrow{b}\) having same magnitude and angle between them is 60° and their scalar product is \({1\over2}\) then \(|\overrightarrow{a}|\) is 

(a)

2

(b)

3

(c)

7

(d)

1