List of top Physics Questions on Vectors

The position vector of a particle related to time t is given by \(\vec{r}=(10t\hat{i}+15t^2\hat{j}+7\hat{k})m\)
The direction of net force experienced by the particle is :

The resultant magnitude of two vectors of same magnitude is equal to magnitude of either. The angle between the two vectors is

The sides of a parallelogram are represented by vectors $$ \vec{p} = 5\hat{i} - 4\hat{j} + 3\hat{k} \quad \text{and} \quad \vec{q} = 3\hat{i} + 2\hat{j} - \hat{k}. $$ Then, the area of the parallelogram is

Two position vectors are given by \[ \vec{r}_1=(1,1,1) \] and \[ \vec{r}_2=(1,-1,1) \] The unit vector in the direction of \[ \vec{r}_1\times \vec{r}_2 \] is

If two vectors \(\vec{A}\) and \(\vec{B}\) are mutually perpendicular, then the component of \(\vec{A}-\vec{B}\) along the direction of \(\vec{A}+\vec{B}\) is:

The component of a vector \[ \vec{P}=3\hat{i}+4\hat{j} \] along the direction \[ \hat{i}+2\hat{j} \] is

The dot product of \((\mathbf{i}+\mathbf{j}+\mathbf{k})\) and the unit vector parallel to \((i-j+k) is:

A vector \(\vec{P}\) directed along the \(x\)-axis is added to vector \(\vec{Q}\) which has a magnitude of \(10\,\text{m}\). The resultant vector is directed along the \(y\)-axis, with a magnitude that is \(2\) times that of \(\vec{P}\). The magnitude of \(\vec{P}\) is

If two vectors P = \(\hat{i} \)+2m\(\hat{j}\)+m\(\hat{k}\) & Q = 4\(\hat{i}\)-2\(\hat{j}\)+m\(\hat{k}\) are perpendicular to each other, then the value of m will be:

Two bodies of mass \(1\) kg and \(3\) kg have position vectors \(\hat i+2\hat j+\hat k\) and \(−3\hat i−2 \hat j+\hat k\), respectively. The magnitude of position vector of centre of mass of this system will be similar to the magnitude of vector.

The component of a vector $ \vec{P} = 3\hat{i} + 4\hat{j} $ along the direction $ \hat{i} + 2\hat{j} $ is

If two vectors $ \vec{A} $ and $ \vec{B} $ are mutually perpendicular, then the component of $ \vec{A} \cdot \vec{B} $ along the direction of $ \vec{A} + \vec{B} $ is

If \(\overrightarrow A=(2\hat i+3\hat j−\hat k)m\) and \(\overrightarrow B=(\hat i+2\hat j+2\hat k)m\). The magnitude of component of vector \(\overrightarrow A\) along vector \(\overrightarrow B\) will be ______\(m\).

The dot product of unit vectors $\hat{n}_1$ and $\hat{n}_2$ that are parallel to $5\hat{i} + 12\hat{j}$ and $3\hat{i} + 4\hat{j}$ respectively is

The resultant of two forces acting at an angle of \( 120^\circ \) is \( 10 \, \text{kg-W} \) and is perpendicular to one of the forces. That force is

The angle between \(\vec{A}\) and the resultant of \(2\vec{A}+3\vec{B}\) and \(4\vec{A}-3\vec{B}\) is

The angle made by a vector \( \vec{B} = 3\hat{i} + 2\hat{j} + 4\hat{k} \) with the y-axis is

If \( \mathbf{A} = \hat{i} + 12 \hat{j} + \hat{k} \) and \( \mathbf{B} = 2\hat{i} - a\hat{j} + \hat{k} \) are perpendicular to each other, then what will be the value of \( a \)?

A simple pendulum of length \( \ell \) has a bob of mass \( m \). It executes S.H.M. of small amplitude \( A \). The maximum tension in the string is

The magnetic susceptibility of a paramagnetic material at \( -73^\circ \text{C} \) is \( 0.0075 \). Its value at \( -173^\circ \text{C} \) will be

The extension in a wire obeying Hooke’s law is \( x \). The speed of sound in the stretched wire is \( V \). If the extension in the wire is increased to \( 4x \), then the speed of sound in the wire is