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#### Vector Algebra - I One Mark Question

11th Standard

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Maths

Time : 00:30:00 Hrs
Total Marks : 10
10 x 1 = 10
1. The value of $\overrightarrow{AB}+\overrightarrow{BC}+\overrightarrow{DA}+\overrightarrow{CD}$ is

(a)

$\overrightarrow{AD}$

(b)

$\overrightarrow{CA}$

(c)

$\overrightarrow{0}$

(d)

$-\overrightarrow{AD}$

2. 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)

$1\over6$

3. 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)

${2\hat{i}-\hat{j}\over\sqrt{5}}$

4. 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°

5. 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)

$-4\hat{i}$

6. 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)

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

7. 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.

8. 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)

$\overrightarrow{0}$

9. 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)

$\overrightarrow{a}+\overrightarrow{b}\over 2$

10. 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)

${\overrightarrow{a}-\overrightarrow{b}\over 3}$