Comparing Vectors

Q. What is the polygon law of vector addition?

Q.

What is the relation between dot product and cross product?

Q. Consider a ring of mass m and radius r maximum gravitational intensity on the axis of the Ring has value

Q. A vector may change if

1. Vector is translated parallel to itself
2. Frame of reference is translated
3. Frame of reference is rotated
4. Vector is rotated

Q. The vector sum of the forces of 10 N and 6 N can be

1. 2 N
2. 8 N
3. 18 N
4. 20 N

Q. The magnitude of scalar product of two vectors is 8 and that of vector product is $8\sqrt{3}$. The angle between them is

1. ${60}^{\circ }$
2. ${30}^{\circ }$
3. ${120}^{\circ }$
4. ${150}^{\circ }$

Q.

Evaluate ${\tan }^{-1}\left(\frac{\mathrm{a}-\mathrm{b}}{1+\mathrm{ab}}\right)+{\tan }^{-1}\left(\frac{\mathrm{b}-\mathrm{c}}{1+\mathrm{bc}}\right)$:

1. ${\tan }^{-1}\mathrm{a}-{\tan }^{-1}\mathrm{b}$

2. ${\tan }^{-1}\mathrm{a}-{\tan }^{-1}\mathrm{c}$

3. ${\tan }^{-1}\mathrm{b}-{\tan }^{-1}\mathrm{c}$

4. ${\tan }^{-1}\mathrm{c}-{\tan }^{-1}\mathrm{a}$

Q.

Which of the following cannot be the resultant of 5 and 10?

1. 5
2. 8
3. 2
4. 7

Q.

If $5cos2\theta +2co{s}^2\frac{\theta }{2}+1=\theta$, where $0<\theta <\mathrm{\pi }$ , then the value of $\theta$

1. $\frac{\pi }{3}\pm \pi$

2. $\frac{\pi }{3},{\cos }^{-1}\left(\frac{3}{5}\right)$

3. ${\cos }^{-1}\left(\frac{3}{5}\right)\pm \pi$

4. $\frac{\pi }{3},\pi –{\cos }^{-1}\left(\frac{3}{5}\right)$

Q.

The unit vector along $i+j$ is

1. $k$

2. $i+j$

3. $\frac{i+j}{\sqrt{2}}$

4. $\frac{i+j}{2}$

Q.

Both the springs shown in figure are unstretched. If the block is displaced by a distance x and released, what will be the initial acceleration ?

Q. Find the vector sum of n coplanar forces, each of magnitude F, when each force is making an angle of 2/n with the preceding one.

Q.

If the angle between the two lines of regression is$90°$, then it represents

1. Perfect correlation

2. Perfect negative correlation

3. No linear correlation

4. None of the above

Q.

The vector sum of the forces of 10 Newton and 6 Newton can be

Q.

If the resultant of two forces is of magnitude $P$ and equal to one of them and perpendicular to it, then the other force is

1. $\sqrt{2}P$

2. $P$

3. $\sqrt{3}P$

4. None of these

Q. The sum!of N coplanar from each other of magnitude F when each force makes an angle (2* pi)/N with the proceeding one??

Q. Which of the following is wrong about the magnitude of the component of a vector?

1. always less than its magnitude
2. may be less than its magnitude
3. may be equal to its magnitude
4. may be equal to zero

Q.

prove the rotation v=w*r

Q.

What is the cross product of two vectors?

Q. Explain vector product of two vector and state their characteristics.

Q. Two wires are made of the same material and have the same volume. The first wire has cross-sectional area $A$ and the second wire has cross-sectional area $3A$. If the length of the first wire is increased by $\Delta l$ on applying a force $F$, how much force is needed to stretch the second wire by the same amount ?

1. $4\text{F}$
2. $6\text{F}$
3. $9\text{F}$
4. $\text{F}$

Q. Two forces are in the ratio of 3:5 give a resultant of 35N. If the angle of inclination be 60°, calculate the magnitude of each force.

Q. Diffrence between vector magnitude and vector .j.k

Q.

What can be the value of the vector sum of the forces 10N and 6N ?

Q. Vector necessarily changed, if it is rotated through an angle.

1. False
2. True

Q. The magnitudes of four pairs of displacement vectors are given. Which pairs of displacement vectors cannot be added to give a resultant vector of magnitude 4$cm$ ?

1. $2cm,3cm$
2. $1cm,3cm$
3. $1cm,5cm$
4. $1cm,7cm$

Q.

Find difference between the given vectors A & B.

1. 

2. 

3. 

4. none of these

Q. The position coordinates of a projectile projected from ground on a certain planet ( with no atmosphere ) are given by y = (4t - 2t^2) m and x= (3t) metre , where t is in second and point of projection is taken as origin. The angle of projection of projectile with the vertical is ?

Q. A block is dragged on smooth plane with the help of a rope which moves with velocity v. The horizontal velocity of the block is :

1. v
2. $vsin\theta$
3. $\frac{v}{cos\theta }$
4. $\frac{v}{sin\theta }$

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

1. $\frac{5}{\sqrt{2}}$
2. $\frac{25}{\sqrt{2}}$
3. $\frac{7}{\sqrt{3}}$
4. none of these