Multiplication with Vectors

Q. A vector $\overrightarrow{A}$ points vertically upward and $\overrightarrow{B}$ point towards north. The vector product $\overrightarrow{A}\times \overrightarrow{B}$ is

1. zero
2. along west
3. along east
4. vertically downwards

Q.

Which of the following is the unit vector perpendicular to $\overrightarrow{A}$ and $\overrightarrow{B}$?

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

Q.

A body constrained to move in the y - direction is subjected to a force given by $\overrightarrow{F}=(-2\hat{i}+15\hat{j}+6\hat{k})N.$ What is the work done by this force in moving the body a distance of $10m$ along the y - axis?

1. $20J$
2. $150J$
3. $190J$
4. $160J$

Q.

How do you find the value of ${\cos }^{-1}\left(0\right)$?

Q.

If $\left|\overrightarrow{A}\times \overrightarrow{B}\right|=\left|\overrightarrow{A}·\overrightarrow{B}\right|$, then angle between $\overrightarrow{A}$ and $\overrightarrow{B}$ will be

1. $30°$

2. $45°$

3. $60°$

4. $90°$

Q. Three vectors $\overrightarrow{P},\overrightarrow{Q}$ and $\overrightarrow{R}$ are such that $|\overrightarrow{P}|=|\overrightarrow{Q}|,|\overrightarrow{R}|=\sqrt{2}|\overrightarrow{P}|$, and $\overrightarrow{P}+\overrightarrow{Q}+\overrightarrow{R}=\overrightarrow{0}$. The angles between $\overrightarrow{P}$ and $\overrightarrow{Q},\overrightarrow{Q}$ and $\overrightarrow{R}$, and $\overrightarrow{P}$ and $\overrightarrow{R}$ are

1. ${90}^{\circ },{135}^{\circ },{135}^{\circ }$
2. ${90}^{\circ },{45}^{\circ },{45}^{\circ }$
3. ${45}^{\circ },{90}^{\circ },{90}^{\circ }$
4. ${45}^{\circ },{135}^{\circ },{135}^{\circ }$

Q. The rectangular components of a vector are $(2,2)$. The corresponding rectangular components of another vector are $(1,\sqrt{3})$ . Find the angle between the two vectors (in degree).

Q.

The principal value of ${\sin }^{-1}\left[\sin \left(\raisebox{1ex}{$2\mathrm{\pi }$}\!\left/ \!\raisebox{-1ex}{$3$}\right.\right)\right]$ is

1. $\raisebox{1ex}{$-2\mathrm{\pi }$}\!\left/ \!\raisebox{-1ex}{$3$}\right.$

2. $\raisebox{1ex}{$2\mathrm{\pi }$}\!\left/ \!\raisebox{-1ex}{$3$}\right.$

3. $\raisebox{1ex}{$4\mathrm{\pi }$}\!\left/ \!\raisebox{-1ex}{$3$}\right.$

4. None of these

Q. What is the angle between $(\overrightarrow{P}+\overrightarrow{Q})$ and $(\overrightarrow{P}\times \overrightarrow{Q})$

1. $0$
2. $\frac{\pi }{4}$
3. $\pi$
4. $\frac{\pi }{2}$

Q. Explain vector product of two vectors.

Q.

A person is holding a bucket by applying a force of $10N$. He moves a horizontal distance of $5m$ and then climbs up a vertical distance of $10m$. The total work done by him is equal to

1. $50J$
2. $150J$
3. $100J$
4. $200J$

Q.

A clock has a continuously moving second’s hand of $0.1m$ length. The average acceleration of the tip of the hand (in units of $m{s}^{-2}$) is of the order of

1. ${10}^{-3}$

2. ${10}^{-1}$

3. ${10}^{-2}$

4. ${10}^{-4}$

Q.

The area of the parallelogram having diagonals $\overrightarrow{a}=3\hat{i}+\hat{j}-2\hat{k}$ and $\overrightarrow{b}=\hat{i}-3\hat{j}+4\hat{k}$ is?

1. $10\sqrt{3}$

2. $5\sqrt{3}$

3. $8$

4. $4$

Q. The vector $\overrightarrow{P}=a\hat{i}+a\hat{j}+3\hat{k}\text{and}\overrightarrow{Q}=a\hat{i}-2\hat{j}-\hat{k}$ are perpendicular to each other. The positive value of $a$ is

1. $3$
2. $4$
3. $9$
4. $1$

Q.

Suppose $\overrightarrow{a}$ is a vector of magnitude 4.5 unit due north. What is the vector (a) 3 $\overrightarrow{a}$, (b) -4 $\overrightarrow{a}$ ?

Q. If $\overrightarrow{P}$ and $\overrightarrow{Q}$ are two non-zero vectors, what is the angle between $(\overrightarrow{P}+\overrightarrow{Q})$ and $(\overrightarrow{P}\times \overrightarrow{Q})$ ?

1. $0$
2. $\frac{\pi }{2}$
3. $\frac{\pi }{4}$
4. $\pi$

Q.

Which value of $\tan$ is $2$?

Q.

Forces of $1,2$unit act along the lines $x=0$ and $y=0$. The equation of the line of action of the resultant is

1. $y–2x=0$

2. $2y–x=0$

3. $y+x=0$

4. $y–x=0$

Q. The unit vector which is perpendicular to the vectors $\overrightarrow{A}=\hat{i}+2\hat{j}-\hat{k}$ and $\overrightarrow{B}=3\hat{i}-2\hat{j}+\hat{k}$ is

1. $(\hat{j}+4\hat{k})$
2. $\frac{1}{\sqrt{5}}(-\hat{j}-2\hat{k})$
3. $(\hat{j}-2\hat{k})$
4. $\frac{1}{\sqrt{5}}(\hat{j}+4\hat{k})$

Q. If $\overrightarrow{A}\times \overrightarrow{B}=\overrightarrow{B}\times \overrightarrow{A}$, then the angle between $\overrightarrow{A}$ and $\overrightarrow{B}$ is

1. $\pi$
2. $\frac{\pi }{4}$
3. $\frac{\pi }{3}$
4. $\frac{\pi }{2}$

Q.

The structure of a water molecule is shown in figure(9-E1).Find the distance of the centre of mass of the molecule from the centre of the oxygen atom.

Q.

The angles which the vector i^+j^+rt2k^ makes withe X, Y and Z axes respectively are

Q.

If $\left|\overrightarrow{A}\right|=2$ and $\left|\overrightarrow{B}\right|=5$ and $\left|\overrightarrow{A}·\overrightarrow{B}\right|=8$, then what is $\overrightarrow{A}·\overrightarrow{B}$ equal to?

1. $6$

2. $2$

3. $20$

4. $8$

Q. The position vector of a particle is given as $\overrightarrow{r}=(t^2-4t+6)\hat{i}+\left(t^2\right)\hat{j}.$ The time after which the velocity vector and acceleration vector becomes perpendicular to each other is equal to

1. $1\text{sec}$
2. $1.5\text{sec}$
3. $\text{Not Possible}$
4. $2\text{sec}$

Q.

What is the direction of the null vector?

Q. Calculate the area of the parallelogram when adjacent sides are given by the vectors $\overrightarrow{A}=2\hat{i}+3\hat{j}+4\hat{k}$ and $\overrightarrow{B}=2\hat{i}-3\hat{j}+\hat{k}$

1. $15\hat{i}+6\hat{j}+12\hat{k}$
2. $15\hat{i}+6\hat{j}-12\hat{k}$
3. $15\hat{i}+16\hat{j}+12\hat{k}$
4. $5\hat{i}+6\hat{j}-12\hat{k}$

Q.

How do you find the last term of an arithmetic progression $?$

Q. Three non-zero vectors $\overrightarrow{A},\overrightarrow{B}$ & $\overrightarrow{C}$ satisfy the relation $\overrightarrow{A}.\overrightarrow{B}=0$ & $\overrightarrow{A}.\overrightarrow{C}=0$. Then $\overrightarrow{A}$ can be parallel to

1. $\overrightarrow{B}$
2. $\overrightarrow{C}$
3. $\overrightarrow{B}.\overrightarrow{C}$
4. $\overrightarrow{B}\times \overrightarrow{C}$

Q.

A vector a has components $3P$ and $1$ with respect to a rectangular Cartesian system. This system is rotated through a certain angle about the origin in the counterclockwise sense. If with respect to the new system, a has components $P+1$ and $\sqrt{10}$, then a value of $P$ is equal to:

1. $1$

2. $-1$

3. $\frac{4}{5}$

4. $-\frac{5}{4}$

Q. Find the projection of $\overrightarrow{A}=2\hat{i}-\hat{j}+\hat{k}$ along the vector $\overrightarrow{B}=\hat{i}+\hat{j}+\hat{k}$.

1. $\frac{2}{\sqrt{3}}$
2. $\frac{1}{\sqrt{3}}$
3. $0$
4. $\frac{4}{\sqrt{3}}$