List of top Physics Questions on Vectors

The area of parallelogram formed by vectors \(\overset{⃗}{P} = 2\hat{i}-\hat{j}+5\hat{k}\) and \(\overset{⃗}{Q} = 3\hat{i}-2\hat{j}+4\hat{k}\) is

If two vectors \(\overset{⃗}{A} = 4\hat{i}+n\hat{j}+2\hat{k}\) and \(\overset{⃗}{B} = 2\hat{i}+2\hat{j}-\hat{k}\) are mutually perpendicular to each other then value of 'n' is

For two vectors \(\overset{⃗}{P}\) and \(\overset{⃗}{Q}\), \(\overset{⃗}{P}\cdot \overset{⃗}{Q} = |\overset{⃗}{P}\times \overset{⃗}{Q}|\)
The magnitude of \(\overset{⃗}{R} = \overset{⃗}{P}+\overset{⃗}{Q}\) is (\(cos45^{\circ} = \frac{1}{\sqrt{2}}\)) ?

If a unit vector is represented by \(\overset{⃗}{U} = 0.9\,\hat{i}-0.2\,\hat{j}+m\hat{k}\), then the value of m is

The angle made by vector \(\overset{⃗}{A} = 2\hat{i}+3\hat{j}\) with x-axis and that with y-axis are respectively.

There are two vectors \(\overset{⃗}{A} = 6\hat{i}+9\hat{j}-\hat{k}\) and \(\overset{⃗}{B} = 2\hat{i}+3\hat{j}-p\hat{k}\) which have the same direction. The value of 'p' is

Resultant of two vectors \(\overset{⃗}{P}\) and \(\overset{⃗}{Q}\) is of magnitude A. If \(\overset{⃗}{Q}\) is reversed, then the resultant is of magnitude B. The value of \(A^2+B^2\) is

Vectors \(a\hat{i}+b\hat{j}+\hat{k}\) and \(2\hat{i}-3\hat{j}+4\hat{k}\) are perpendicular to each other when \(3a+2b = 7\), the ratio of a to b is \(x/2\). The value of x is

Let \(\overset{⃗}{P} = \hat{i}+\hat{j}+\hat{k}\) and \(\overset{⃗}{Q} = -(\hat{i}+\hat{j}+\hat{k})\). The angle between \((\overset{⃗}{P}-\overset{⃗}{Q})\) and \(\overset{⃗}{P}\) is

Let \(\overset{⃗}{A}\) and \(\overset{⃗}{B}\) are two non-zero vectors of different magnitude. Which one of the following is the correct equation ?

A vector \(\overset{⃗}{A}\) when added to the sum of the vectors \((\hat{i}-2\hat{j}+2\hat{k})\) and \((-2\hat{i}+\hat{j}-\hat{k})\) gives a unit vector along Y axis. The magnitude of vector \(\overset{⃗}{A}\) is

Calculate the values of \(a\) and \(b\) if vectors \(a\hat{i}+b\hat{j} = \hat{n}\) and \((\hat{i}+\hat{j})\) are perpendicular to each other

The vector sum of the two forces \(\overset{⃗}{A}\) and \(\overset{⃗}{B}\) is perpendicular to their vector difference. Hence forces \(\overset{⃗}{A}\) and \(\overset{⃗}{B}\) are

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

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

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

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)