Question 1 :
A vector $C$ when added to vectors $A=3\widehat{i}-5\widehat{j}+\widehat{k}$ and $B=2\widehat{i}+3\widehat{j}-4\widehat{k}$ gives a unit vector along the y-axis. Then, $C$ is

Question 2 :
Which of the following operations between the two vectors can yield a vector perpendicular to either of them?<p></p>

Question 3 :
If $|\overline{\mathrm{a}}\times\overline{b}|=|\overline{\mathrm{a}} \cdot \overline{b}|$, then the angle between $\overline{\mathrm{a}}$ and $\overline{b}$ is:<br/>

Question 4 :
The unit vector perpendicular to both of the vectors 2 $\hat{i}-\hat{j}+\hat{k}$ and $3\hat{i}+4\hat{j}-\hat{k}$ is<br/>

Question 5 :
The number of vectors of unit length perpendicular to the vectors $\vec { a } =\hat { i } +\hat { j } $ and $\vec { b } =\hat { j } +\hat { k } $, is

Question 6 :
If a person $A$ is moving with velocity $2Km/h$, person $B$ is moving withe velocity $3km/h$ and the angle between the direction of movements of $A$ and $B$ is ${60}^{o}$, then the velocity of $A$ relative to $B$ in the direction of $A$ is

Question 7 :
A unit vector parallel to $xy$-plane and perpendicular to the vector $4\hat{i}-3\hat{j}+\hat{k}$ is<span><br/></span>

Question 8 :
Find how the total acceleration $\omega$ of the balloon depends on the height of ascent.

Question 10 :
A ship moves along the equator to the east with a speed $30\ km/h$. Southeastern wind blows ${ 60 }^{ \circ }$ to the east with $15\ km{ h }^{ -1 }$. Find the wind velocity relative to the ship.<br/>

Question 11 :
Find the displacement covered by the bolt during the free fall in the reference frame fixed to the elevator shaft.

Question 12 :
If $\vec{OA}=\hat{i}-\hat{j}$ and $\vec{OB}=\hat{j}-\hat{k}$, then a unit vector parpendicular to the plane $AOB$ is<br/>

Question 13 :
The distance travelled by the car, if a car travels $4\ km$ towards north at an angle of $45^{\circ}$ to the east and then travels a distance of $2\ km$ towards north at an angle of $135^{\circ}$ to the east, is

Question 14 :
The plane which can be formed with the vectors $\overline{a}=3\overline{i}-4\overline{j}+2\overline{k},\ \overline{b}=2\overline{i}-\overline{j}-6\overline{k}$,$\overline{c}=5\overline{i}-5\overline{j}-4\overline{k}$ is<br/>

Question 16 :
Which of the following algebraic operations with scalar and vector physical quantities are meaningful.<div><br/>(i) adding any two vectors<br/>(ii) adding a scalar to a vector of the same dimensions<br/>(iii) multiplying any vector by any scalar<br/>(iv) multiplying any two scalars<br/>(v) adding any two scalars<br/>(vi) adding a component of a vector to the same vector.</div>

Question 17 :
Match vector operations between two vectors A and B in column I with angles between the two vectors in column II : <table class="wysiwyg-table"><tbody><tr><td>Column-I</td><td>Column-II</td></tr><tr><td>$\mathrm{a})|\vec{\mathrm{A}}+\vec{\mathrm{B}}|=|\vec{\mathrm{A}}-\vec{\mathrm{B}}|$</td><td>e) $45^{0}$</td></tr><tr><td>$\mathrm{b}) |\vec{\mathrm{A}}\times\vec{\mathrm{B}}|=\vec{\mathrm{A}}.\vec{\mathrm{B}}$ </td><td>f) $30^{0}$</td></tr><tr><td>$\mathrm{c}) \displaystyle \vec{\mathrm{A}}.\vec{\mathrm{B}}=\frac{\mathrm{A}\mathrm{B}}{2}$</td><td>g) $90^{0}$</td></tr><tr><td>$\mathrm{d}) |\displaystyle \vec{\mathrm{A}}\times\vec{\mathrm{B}}|=\frac{\mathrm{A}\mathrm{B}}{2}$ </td><td>h) $60^{0}$</td></tr></tbody></table>

Question 18 :
X-component of $\vec{a}$ is twice of its Y-component. If the magnitude of the vector is $5\sqrt{2}$ and it makes an angle of $135^{\circ}$ with z-axis then the components of vector is

Question 19 :
The vector that must be added to the vector $\hat{i}-3\hat{j}+2\hat{k}$ and $3\hat{i}+6\hat{j}-7\hat{k}$ so that the resultant vector is a unit vector along the y-axis is:

Question 20 :
A man travels $1 \: mile$ due east, $5 \: mile$ due south, $2 \:mile$ due east and finally $9\: miles$ due north. How far is the starting point?<p></p>