List of top Physics Questions on Vectors

A vector is given as $\vec{A} = 3\hat{j} - 4\hat{k}$. The vector parallel to $\vec{A}$ and magnitude the same as that of the vector $\hat{i} - 2\hat{j}$ is

For what value of \(x\), will the two vectors \[ \vec A=\hat i+4\hat j-2\hat k \] \[ \vec B=-2\hat i+x\hat j-x^2\hat k \] be mutually perpendicular?

Which of the following statements is/are true?
• [(A)] Three vectors not lying in a plane give zero resultant
• [(B)] Three vectors lying in a plane can give zero resultant
• [(C)] Two vectors of different magnitude can be combined to give a zero resultant

If the vectors $\vec{A}=a_{x}\hat{i}+a_{y}\hat{j}+a_{z}\hat{k}, \vec{B}=b_{x}\hat{i}+b_{y}\hat{j}+b_{z}\hat{k}$ and $\vec{C}=c_{x}\hat{i}+c_{y}\hat{j}+c_{z}\hat{k}$ are defining the vector $\vec{T}=\vec{A}-\vec{B}+\vec{C}$ then the z-component of the vector $T_{z}$ is

If the magnitude of the vector \(\vec{P} = x\hat{i} + 0.8\hat{j} + 0.6\hat{k}\) is 2, then the value of x is.

If the scalar product of two vectors $x\hat{i} + 3\hat{j} + 2\hat{k}$ and $2\hat{i} - 3\hat{j} + 4\hat{k}$ is 9, then the value of $x$ is:

A vector \(\sqrt{3}\hat{i} + \hat{j}\) rotates about its tail through an angle 30\(^\circ\) in clock wise direction then the new vector is

A unit vector in the direction of resultant vector of \[ \mathbf{A} = -2\hat{i} + 3\hat{j} + \hat{k}, \quad \mathbf{B} = \hat{i} + 2\hat{j} - 4\hat{k} \] is

If $|\vec{a}| = \sqrt{26}$, $|\vec{b}| = 7$, $|\vec{a} \times \vec{b}| = 35$, find $\vec{a} \cdot \vec{b}$

The vector sum of two forces $\vec{A}$ and $\vec{B}$ is perpendicular to their vector difference. Hence forces $\vec{A}$ and $\vec{B}$ are}

Two capacitors of \( 100 \mu\text{F} \) and \( 50 \mu\text{F} \) are connected in parallel. If the potential difference across \( 100 \mu\text{F} \) is 20 V and across \( 50 \mu\text{F} \) is 40 V, then the common potential of the parallel combination will be (same polarities of the capacitor connected together)

Select the correct statement.

The resultant of two vectors $\vec{A}$ and $\vec{B}$ is $\vec{C}$. If the magnitude of $\vec{B}$ is doubled, the new resultant vector becomes perpendicular to $\vec{A}$, then the magnitude of $\vec{C}$ is

Two vectors \(a\hat{i} + b\hat{j} + \hat{k}\) and \(2\hat{i} - 3\hat{j} + 4\hat{k}\) are perpendicular. When \(3a + 2b = 7\) , the ratio \(a/b\) is \(x/2\). The value of \(x\) is.

If $\vec{A} = \hat{i} + \hat{j} + 3\hat{k}$, $\vec{B} = -\hat{i} + \hat{j} + 4\hat{k}$ and $\vec{C} = 2\hat{i} - 2\hat{j} - 8\hat{k}$, then the angle between the vectors $\vec{P} = \vec{A} + \vec{B} + \vec{C}$ and $\vec{Q} = (\vec{A} \times \vec{B})$ is (in degree)}

Let '\(W\)' joule be the work done to move an electric charge '\(q\)' coulomb from a place \(A\), where potential is \(-5\text{ volt}\) to another place \(B\) where potential is '\(V\)' volt. The value of '\(V\)' is

Four particles each of mass \(M\) are placed at the corners of a square of side \(L\). The radius of gyration of the system about an axis perpendicular to the square and passing through its centre is

Two vectors \(a\hat{i} + b\hat{j} + \hat{k}\) and \(2\hat{i} - 3\hat{j} + 4\hat{k}\) are perpendicular. When \(3a + 2b = 7\) , the ratio \(a/b\) is \(x/2\). The value of \(x\) is.

The resultant of two vectors $\vec{A}$ and $\vec{B}$ is $\vec{C}$. If the magnitude of $\vec{B}$ is doubled, the new resultant vector becomes perpendicular to $\vec{A}$, then the magnitude of $\vec{C}$ is

Among the following pairs of vectors, if the resultant of two vectors can never have magnitude 4 units, the magnitudes of the vectors are

Initially \( n \) identical capacitors are joined in parallel and are charged to potential V. Now they are separated and joined in series. Then}

Which of the following molecules contains maximum number of electrons in antibonding molecular orbitals?

A point marked on a ring of radius \(2\,\text{cm}\) is in contact with a horizontal plane. Now the ring is rolled forward half a revolution along the positive X direction. Then the angle made by the displacement vector of the point with the X-axis is:

Two vectors \(a\hat{i} + b\hat{j} + \hat{k}\) and \(2\hat{i} - 3\hat{j} + 4\hat{k}\) are perpendicular. When \(3a + 2b = 7\) , the ratio \(a/b\) is \(x/2\). The value of \(x\) is.