List of top Physics Questions on Vectors

If any two rows (or columns) of a determinant are identical then the value of the determinant is:
The eigen values of matrix \(A\) are 1, -2, 3. The eigen values of \(3I - 2A + A^2\) are:
A. 2
B. 6
C. 8
D. 11
Choose the correct answer from the options given below:

Match the LIST-I with LIST-II

LIST-I (Expressions)LIST-II (Values)
A.\( i^{49} \)I.1
B.\( i^{38} \)II.\(-i\)
C.\( i^{103} \)III.\(i\)
D.\( i^{92} \)IV.\(-1\)


Choose the correct answer from the options given below:

The real and imaginary parts of \(\log(x+iy)\) are:
If \(\vec{A}=\vec{\nabla}\phi\) and \(\phi = xy+yz+zx\), then the true statements are:
A. \(\vec{\nabla}\cdot\vec{A}=0\)
B. \(\vec{\nabla}\cdot\vec{A}\neq0\)
C. \(\vec{\nabla}\times\vec{A}=\vec{0}\)
D. \(\vec{\nabla}\times\vec{A}\neq\vec{0}\)
Choose the correct answer from the option given below:
The projection of vector \(\vec{A}=\hat{i}-2\hat{j}+\hat{k}\) on vector \(\vec{B}=4\hat{i}-4\hat{j}+7\hat{k}\) is:
If \(\vec{A} = \vec{\nabla} \times \vec{F}\), then \(\oiint_S \vec{A} \cdot \hat{n} dS\) (for any closed surface S) is:
If \(|\vec{A}+\vec{B}| = |\vec{A}-\vec{B}|\) then the angle between vectors \(\vec{A}\) and \(\vec{B}\) is:
For a force F to be conservative, the relations to be satisfied are:
A. \(\frac{\partial F_y}{\partial x} - \frac{\partial F_x}{\partial y} = 0\)
B. \(\frac{\partial F_z}{\partial y} - \frac{\partial F_y}{\partial z} = 0\)
C. \(\frac{\partial F_x}{\partial z} - \frac{\partial F_z}{\partial x} = 0\)
D. \(\frac{\partial F_y}{\partial x} - \frac{\partial F_x}{\partial y} = \frac{\partial F_z}{\partial y} - \frac{\partial F_y}{\partial z} = \frac{\partial F_x}{\partial z} - \frac{\partial F_z}{\partial x} \neq 0\)
Choose the correct answer from the options given below:
Projection of 2\(\hat i\)+4\(\hat j\)−2\(\hat k\) on \(\hat i\)+2\(\hat j\)−α\(\hat k\) is zero. Then, the value of α will be________.

Assertion A : If A, B, C, D are four points on a semi-circular arc with centre at 'O' such that $|\vec{AB}| = |\vec{BC}| = |\vec{CD}|$, then $\vec{AB} + \vec{AC} + \vec{AD} = 4\vec{AO} + \vec{OB} + \vec{OC}$ 
Reason R : Polygon law of vector addition yields $\vec{AB} + \vec{BC} + \vec{CD} = \vec{AD} = 2\vec{AO}$ 

Statement I : Two forces \((\vec{p} + \vec{q})\) and \((\vec{p} - \vec{q})\) where \(\vec{p} \perp \vec{q}\), when act at an angle \(\theta_1\) to each other, the magnitude of their resultant is \(\sqrt{3(p^2 + q^2)}\), when they act at an angle \(\theta_2\), the magnitude of their resultant becomes \(\sqrt{2(p^2 + q^2)}\). This is possible only when \(\theta_1<\theta_2\).
Statement II : In the situation given above, \(\theta_1 = 60^{\circ}\) and \(\theta_2 = 90^{\circ}\).
In the light of the above statements, choose the most appropriate answer from the options given below :

The magnitude of vectors \(\vec{OA}\), \(\vec{OB}\) and \(\vec{OC}\) in the given figure are equal. The direction of \(\vec{OA} + \vec{OB} - \vec{OC}\) with x-axis will be : 

The resultant of these forces \(\vec{OP}, \vec{OQ}, \vec{OR}, \vec{OS}\) and \(\vec{OT}\) is approximately ________ N. 
[Take \(\sqrt{3} = 1.7, \sqrt{2} = 1.4\). Given \(\hat{i}\) and \(\hat{j}\) unit vectors along x, y axis] 

 

In an octagon ABCDEFGH of equal side, what is the sum of $\vec{AB} + \vec{AC} + \vec{AD} + \vec{AE} + \vec{AF} + \vec{AG} + \vec{AH}$, if $\vec{AO} = 2i + 3j - 4k$?

Match List I with List II. 

Choose the correct answer from the options given below :