Mathematics in Physics

The sum of two forces $\vec{P}$ and $\vec{Q}$ is $\vec{R}$ such that $\left|\vec{R}\right|=\left|\vec{P}\right|$. Find the angle between resultant of $2\vec{P}$ and $\vec{Q}$and$\vec{Q}$ , ________

The magnitude of vectors $\vec{\mathrm{OA}},\vec{\mathrm{OB}}$ and $\vec{\mathrm{OC}}$ in the given figure areequal. The direction of $\vec{\mathrm{OA}}+\vec{\mathrm{OB}}-\vec{\mathrm{OC}}$ with $x-$axis will be:

The resultant of two vectors $\vec{A}$ and $\vec{B}$ is perpendicular to $\vec{A}$ and its magnitude is half that of $\vec{B}$. The angle between vectors $\vec{A}$ and $\vec{B}$ is ______ $\circ$?

A vector $\vec{A}$ is rotated by a small angle $\Delta\,\theta\,$ radians $\left(\Delta\,\theta\,\ll\,1\right)$ to get a new vector $\vec{B}$ . In that case $\left|\vec{B}-\vec{A}\right|$ is :

Statement I: If three forces $\vec{F}_{1},\vec{F}_{2}$ and $\vec{F}_{3}$ are represented by three sides of a triangle and $\vec{F_{1}}+\vec{F_{2}}=-\vec{F}_{3},$then these three forces are concurrent forces and satisfy…

$\mathrm{Assertion}A:$ If $A,B,C,D$ are four points on a semi-circular arc with a centre at $O$ such that $|\vec{AB}|=|\vec{BC}|=|\vec{CD}|.$Then,$\vec{AB}+\vec{AC}+\vec{AD}=4\vec{AO}+\vec{OB}+\vec{OC}$…

A person moved from $A$to $B$ on a circular path as shown in figure. If the distance travelled by him is $60m$, then the magnitude of displacement would be : (Given $\cos\,135^{\circ}=-0.7$)

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]

Statement-I : Two forces $\left(\vec{P}+\vec{Q}\right)$ and $\left(\vec{P}-\vec{Q}\right)$ where $\vec{P}\perp\,\vec{Q},$when act at an angle $\theta\,_{1}$ each other, the magnitude of their resultant is…

Three vectors $\overrightarrow{\mathrm{OP}}, \overrightarrow{\mathrm{OQ}}$ and $\overrightarrow{\mathrm{OR}}$ each of magnitude $\mathrm{A}$ are acting as shown in figure. The resultant of the three vectors is…

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, $\vec{\mathrm{AO}}=2\hat{i}+3\hat{j}-4\hat{k}$

The density of a solid metal sphere is diameter. The maximum error in the density of the sphere is$\left(\frac{x}{100}\right)%.$ If the relative errors in measuring the mass and the diameter are…