#### 11th Standard Maths Vector Algebra - I English Medium Free Online Test One Mark Questions 2020 - 2021

11th Standard

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Maths

Time : 00:10:00 Hrs
Total Marks : 10

Answer all the questions

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. 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)

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

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.

4. 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)

$17\over4$

5. 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)

$\frac { 1 }{ 2 } \sqrt { 229 }$

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

7. 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)

$\frac { 5\pi }{ 2 }$

8. 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)

$\pm \frac { 1 }{ {2 } }$

9. 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

10. 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