Unit Vectors

Q.

If $\overrightarrow{P}\times \overrightarrow{Q}=\overrightarrow{Q}\times \overrightarrow{P}$, the angle between $\overrightarrow{P}$ and $\overrightarrow{Q}$ is $\theta (0°<\theta <360°)$, The value of $\theta$ will be

Q.

If $\overrightarrow{P}.\overrightarrow{Q}=PQ$ then the angle between $\overrightarrow{P}\text{and}\overrightarrow{Q}$

1. $\begin{array}{l}0°\end{array}$

2. $\begin{array}{l}30°\end{array}$

3. $45°$

4. $60°$

Q.

A vector is represented by $3\hat{i}+\hat{j}+2\hat{k}$. Its length in $X-Y$ plane is

1. $2$

2. $\sqrt{14}$

3. $\sqrt{10}$

4. $\sqrt{5}$

Q.

How to find the magnitude of the vector?

Q.

If you have three unit vectors such that two of them are along the coordinate axis, is it possible for the resultant to be a unit vector?

1. Yes

2. No

Q.

If $a,b$ and $c$are unit vectors such that$ax(bxc)=\frac{1}{2}b$, then the angle between $a$and $c$ is?

1. $\pi /6$

2. $\pi /4$

3. $\pi /2$

4. $\pi /3$

Q.

If a unit vector is represented by $0.5\hat{i}+0.8\hat{j}+c\hat{k}$, then the value of ‘c’ is

1. 1

2. $\sqrt{0.11}$

3. $\sqrt{0.01}$
   

4. $\sqrt{0.39}$
   

Q.

Which of these are unit vectors

1. $\hat{i}$

2. $\hat{i}+\hat{j}+\hat{k}$

3. $\left(\frac{\hat{i}}{\sqrt{2}}\right)+\left(\frac{\hat{j}}{\sqrt{2}}\right)$

4. $\left(\frac{4}{5}\right)\hat{i}+\left(\frac{3}{5}\right)\hat{j}$

Q. Given $A=2\hat{i}+3\hat{j}$ and $B=\hat{i}+\hat{j}$. The component of vector A along vector B is

1. $\frac{1}{\sqrt{2}}$
2. $\frac{3}{\sqrt{2}}$
3. $\frac{5}{\sqrt{2}}$
4. $\frac{7}{\sqrt{2}}$

Q. If $\overrightarrow{A}+\overrightarrow{B}$ is a unit vector along y - axis and $\overrightarrow{A}=\hat{i}-\hat{j}+\hat{k}$, then what is $\overrightarrow{B}$?

1. $\hat{j}+\hat{k}$
2. $\hat{j}-\hat{k}$
3. $\hat{i}+\hat{j}+\hat{k}$
4. $-\hat{i}+2\hat{j}-\hat{k}$

Q. The unit vector in the direction of $2\hat{i}+3\hat{j}+\hat{k}$ is

1. $\frac{2\hat{i}+3\hat{j}+\hat{k}}{\sqrt{14}}$
2. $\frac{2\hat{i}+\hat{j}+3\hat{k}}{\sqrt{14}}$
3. $\frac{2\hat{i}+3\hat{j}+\hat{k}}{\sqrt{12}}$
4. $\frac{3\hat{i}+2\hat{j}+\hat{k}}{\sqrt{14}}$

Q. If a unit vector is represented by $0.5\hat{i}+0.8\hat{j}+c\hat{k}$ , then the value of $\text{‘}{c}^{\prime }$ is

1. $1$
2. $\sqrt{0.11}$
3. $\sqrt{0.01}$
4. $\sqrt{0.39}$

Q.

Unit vector parallel to the resultant of vectors $\overrightarrow{A}=4\hat{i}-3\hat{j}$ and $\overrightarrow{B}=8\hat{i}+8\hat{j}$

1. $\frac{24\hat{i}+5\hat{j}}{13}$

2. $\frac{12\hat{i}+5\hat{j}}{13}$

3. $\frac{6\hat{i}+5\hat{j}}{13}$

4. $Noneofthese$

Q. The unit vector along $\overrightarrow{A}=2\hat{i}+3\hat{j}$ is

1. $\hat{i}+3\hat{j}$
2. $\frac{2\hat{i}+3\hat{j}}{2}$
3. $\frac{2\hat{i}+3\hat{j}}{3}$
4. $\frac{2\hat{i}+3\hat{j}}{\sqrt{13}}$

Q. Unit vector perpendicular to both$\overrightarrow{A}$ and $\overrightarrow{B}$ is

1. $\frac{\overrightarrow{A}\times \overrightarrow{B}}{|\overrightarrow{A}||\overrightarrow{B}|}$
2. $\frac{\overrightarrow{A}\cdot \overrightarrow{B}}{|\overrightarrow{A}||\overrightarrow{B}|\cos \theta }$
3. $\frac{\overrightarrow{A}\times \overrightarrow{B}}{|\overrightarrow{A}||\overrightarrow{B}|\sin \theta }$
4. $\frac{\overrightarrow{A}\cdot \overrightarrow{B}}{|\overrightarrow{A}||\overrightarrow{B}|\sin \theta }$

Q. A particle is moving with speed $6m/s$ along the direction of $\overrightarrow{A}=2\hat{i}+2\hat{j}-\hat{k}$, find the velocity (in $m/s$).

1. $(4\hat{i}+4\hat{j}-2\hat{k})$
2. $(2\hat{i}+2\hat{j}-\hat{k})$
3. $(8\hat{i}+8\hat{j}-4\hat{k})$
4. $(\hat{i}+\hat{j}-\hat{k})$

Q. If $\hat{i}$ and $\hat{j}$ are unit vectors along x – axis and y – axis respectively, the magnitude of vector $\hat{i}$ + $\hat{j}$ will be

1. 1
2. $\sqrt{2}$
3. $\sqrt{3}$
4. 2

Q.

What is the angle between the following vectors?

$\overrightarrow{A}=3\hat{i}-2\hat{j}+\hat{k}$

$\overrightarrow{B}=2\hat{i}+6\hat{j}-6\hat{k}$

1. 

2. 

3. 

4. None of these

Q.

The sum of vectors A, D and E will be

1. vector D

2. none of these

3. vector E

4. vector A

Q.

Add the following vectors:

$\overrightarrow{A}=5\hat{i}+6\hat{j}-10\hat{k}$

$\overrightarrow{B}=-10\hat{i}-6\hat{j}+10\hat{k}$

1. 

2. 

3. 

4. Both a and b

Q. If a unit vector is represented by $0.5\hat{i}+0.8\hat{j}+c\hat{k}$ , then the value of $\text{‘}{c}^{\prime }$ is

1. $1$
2. $\sqrt{0.11}$
3. $\sqrt{0.01}$
4. $\sqrt{0.39}$

Q. With respect to a rectangular cartesian co-ordinate system three vectors are expressed as $\overrightarrow{a}=4\hat{i}-\hat{j},\overrightarrow{b}=-3\hat{i}+2\hat{j}$ and $\overrightarrow{c}=-\hat{k}$ where $\hat{i},\hat{j}$ and $\hat{k}$ are unit vectors along the x, y, z axes respectively. The unit vector along the direction of sum of these vectors is

1. $\hat{r}=\frac{1}{\sqrt{3}}(\hat{i}+\hat{j}-\hat{k})$
2. $\hat{r}=\frac{1}{\sqrt{2}}(\hat{i}+\hat{j}-\hat{k})$
3. $\hat{r}=\frac{1}{3}(\hat{i}+\hat{j}+\hat{k})$
4. $\hat{r}=\frac{1}{\sqrt{3}}(\hat{i}+\hat{j}+\hat{k})$

Q. Value of C may be, if $\overrightarrow{A}=\frac{2\hat{i}}{5}-\frac{\hat{j}}{5}+\frac{C\hat{k}}{5}$ is a unit vector.

1. $\sqrt{20}$
2. $\sqrt{10}$
3. 20
4. 5

Q. Given that $0.2\hat{i}+0.6\hat{j}+a\hat{k}$ is a unit vector. What is the value of a?

1. $\sqrt{0.3}$
2. $\sqrt{0.4}$
3. $\sqrt{0.6}$
4. $\sqrt{0.8}$

Q. With respect to a rectangular cartesian co-ordinate system three vectors are expressed as $\overrightarrow{a}=4\hat{i}-\hat{j},\overrightarrow{b}=-3\hat{i}+2\hat{j}$ and $\overrightarrow{c}=-\hat{k}$ where $\hat{i},\hat{j}$ and $\hat{k}$ are unit vectors along the x, y, z axes respectively. The unit vector along the direction of sum of these vectors is

1. $\hat{r}=\frac{1}{\sqrt{3}}(\hat{i}+\hat{j}-\hat{k})$
2. $\hat{r}=\frac{1}{\sqrt{2}}(\hat{i}+\hat{j}-\hat{k})$
3. $\hat{r}=\frac{1}{3}(\hat{i}+\hat{j}+\hat{k})$
4. $\hat{r}=\frac{1}{\sqrt{3}}(\hat{i}+\hat{j}+\hat{k})$