Vectors and Its Types

Q.

State the law of conservation of angular momentum and explain with a suitable example.

Q. \(\text{Assertion A}\) : If \(A, ~B, ~C, ~D\) are four points on a semi-circular arc with centre at \(O\) such that \(|\overrightarrow {AB}|=|\overrightarrow {BC}|=|\overrightarrow {CD}|\), then \(\overrightarrow {AB}+\overrightarrow {AC}+\overrightarrow {AD}=4~\overrightarrow {AO}+\overrightarrow {OB}+\overrightarrow {OC}\)

\(\text{Reason R}\) : Polygon law of vector addition yields
\(\overrightarrow {AB}+\overrightarrow {BC}+\overrightarrow {CD}=\overrightarrow {AD}=2~\overrightarrow {AO}\)


In the light of the above statements, choose the most appropriate answer from the options given below :

Q.

Why do we use $ijk$ for vectors?

Q. What is trajectory?

Q. Six forces 9.81 N each, acting at a point are coplanar. If the angles between neighbouring forces are equal, then the resultant is

1. $2\times 9.81N$
2. $3\times 9.81N$
3. 9.81 N
4. 0 N

Q. What is the angle between a vector and its negative vector?

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

Q.

What is the right hand screw rule in case of cross product?

Q.

What is null vector?

Q.

Is volume a vector quantity?

Q. A change in a vector may occur due to rotation of frame of reference. Explain.

Q.

What is a tensor ?is time scalar or vector?

Q. Match List-I with List-II

List-I	List-II
(a) $\overrightarrow{C}-\overrightarrow{A}-\overrightarrow{B}=0$	(i)
(b) $\overrightarrow{A}-\overrightarrow{C}-\overrightarrow{B}=0$	(ii)
(c) $\overrightarrow{B}-\overrightarrow{A}-\overrightarrow{C}=0$	(iii)
(d) $\overrightarrow{A}+\overrightarrow{B}=\overrightarrow{C}$	(iv)

Choose the correct answer from the options given below:

1. $\left(a\right)\to \left(iv\right),\left(b\right)\to \left(iii\right),\left(c\right)\to \left(i\right),\left(d\right)\to \left(ii\right)$
2. $\left(a\right)\to \left(iv\right),\left(b\right)\to \left(i\right),\left(c\right)\to \left(iii\right),\left(d\right)\to \left(ii\right)$
3. $\left(a\right)\to \left(iii\right),\left(b\right)\to \left(ii\right),\left(c\right)\to \left(iv\right),\left(d\right)\to \left(i\right)$
4. $\left(a\right)\to \left(i\right),\left(b\right)\to \left(iv\right),\left(c\right)\to \left(ii\right),\left(d\right)\to \left(iii\right)$

Q. What is a vector quantity?

Q.

Which of the following is not a vector quantity?

1. Weight

2. Nuclear spin

3. Momentum

4. Potential energy

Q.

Is the position a vector or scalar?

Q. What is the angle between a vector and its negative vector?

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

Q. A weight $W$ is supported by two strings inclined at ${60}^{\circ }$ and ${30}^{\circ }$ to vertical. The tensions in the strings are $T_1$ and $T_2$ as shown. If these tensions have to be determined in terms of $W$ using a triangle of forces, then which of the following triangles should be drawn ?
(The blocks in equilibrium)

1. 
2. 
3. 
4. 

Q. The displacement x of a partical along x-axis is given by x=3 +8t +7t (sq) obtain it's velocity and acceleration at t =2s

Q.

Which of these are vector quantities, distance, displacement, speed, and velocity?

Q.

What is lateral stress?

Q. A change in a vector may occur due to rotation of the vector. Explain.

Q. Two vectors of the same physical quantity are unequal if

1. they have the same magnitude and the same direction
2. they have different magnitudes but the same direction
3. they have the same magnitude but different directions
4. they have different magnitudes and different directions.

Q. The vector $-\overrightarrow{A}$ is

1. in the direction opposite to $\overrightarrow{A}$
2. greater than $\overrightarrow{A}$ in magnitude
3. less than $\overrightarrow{A}$ in magnitude
4. in the same direction as $\overrightarrow{A}$

Q. Why do we use vectors?

Q.

Does the angular momentum of a body in translatory motion is zero$?$

Q. Can we add a velocity vector to a displacement vector?

Q.

The distance between the directrices of the hyperbola $x=8\sec \theta ,y=8\tan \theta$ is

1. $8\sqrt{2}$

2. $16\sqrt{2}$

3. $4\sqrt{2}$

4. $6\sqrt{2}$

Q. The angle between vector $\overrightarrow{A}$ and $-2\overrightarrow{A}$ is

1. $0^{\circ }$
2. ${180}^{\circ }$
3. ${360}^{\circ }$
4. ${90}^{\circ }$

Q. When two vectors lie in a plane, then these vectors are called

1. coplanar
2. collinear
3. null
4. parallel

Q.

Do speed and velocity has the same dimension? How?