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)

\(1\over6\)

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)

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

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)

\(\overrightarrow{0}\)

If \(\overrightarrow{a},\overrightarrow{b}\) are the position vectors A and B, then which one of the following points whose position vector lies on AB, is

(a)

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

(b)

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

(c)

\({2\overrightarrow{a}+\overrightarrow{b}\over 3}\)

(d)

\({\overrightarrow{a}-\overrightarrow{b}\over 3}\)

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

Two vertices of a triangle have position vectors \(3\hat{i}+4\hat{j}-4\hat{k}\) and \(2\hat{i}+3\hat{j}+4\hat{k}\) . If the position vector of the centroid is \(\hat{i}+2\hat{j}+3\hat{k}\), then the position vector of the third vertex is

(a)

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

(b)

\(-2\hat{i}-\hat{j}-6\hat{k}\)

(c)

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

(d)

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

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

If \(|\overrightarrow{a}|=13,|\overrightarrow{b}|=5\)  and \(\overrightarrow{a}.\overrightarrow{b}=60^o\) then \(|\overrightarrow{a}\times\overrightarrow{b}|\) is

(a)

15

(b)

35

(c)

45

(d)

25

If   \(\overrightarrow{a}\)  and   \(\overrightarrow{b}\) are two vectors of magnitude 2 and inclined at an angle 60°, then the angle between   \(\overrightarrow{a}\)  and \(\overrightarrow{a}+\overrightarrow{b}\) is

(a)

30°

(b)

60°

(c)

45°

(d)

90°

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)

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