Scalars and Vectors

The magnitudes of vectors  $\overrightarrow{A},\overrightarrow{B}\mathrm{and}\overrightarrow{C}$  are $3,$ $4$ and $5$ units respectively. If  $\overrightarrow{A}+\overrightarrow{B}=\overrightarrow{C}$ , then the angle between  $\overrightarrow{A}\mathrm{and}\overrightarrow{B}$  is :

Rain is falling vertically downwards with a speed $5 \raisebox{1ex}{$\mathrm{m}$}\!\left/ \!\raisebox{-1ex}{$\mathrm{s}$}\right.$. If unit vector along upward is defined as $\hat{\mathrm{j}}$, represent velocity of rain in vector form.

A man weighing $50 \mathrm{kg}$ walk along a rope tied between two pegs which are $20 \mathrm{m}$ apart horizontally. When he comes to the middle point of the rope it sags by $0.875 \mathrm{m}$. Calculate the tension in the string.

$P$ and $2P$ are two forces acting on a particle. When the first force is increased by $20 \mathrm{kg} \mathrm{wt}$ and second is double, the direction of the resultant remains unaltered. Find $P$.

A body of mass $6 \mathrm{kg}$ is suspended by two strings of length $4 \mathrm{m}$ and $3 \mathrm{m}$ attached to two points $5 \mathrm{m}$ apart in the same horizontal line. Find the tensions in the strings.

The greatest and least resultant of two forces acting at a point in $29 \mathrm{kg}$ wt and $5 \mathrm{kg}$ wt respectively. If each force is increased by $3 \mathrm{kg}$wt, find the magnitude of the resultant of two new forces when acting to the at right angles to each other.

A uniform rod of length $5 \mathrm{m}$ weighing $5 \mathrm{kg}$ is suspended from a fixed point using strings of length $3 \mathrm{m}$ and $4 \mathrm{m}$ attached to its ends. What is the inclination of the rod to the vertical?

What are the conditions for the equilibrium of a rigid body under the action of coplanar forces?

Obtain the condition for equilibrium of colinear forces.

State and prove the parallelogram law of forces.

A particle is moving at $5 \mathrm{m} {\mathrm{s}}^{-1}$ towards east. In one second its velocity changes to $5 \mathrm{m} {\mathrm{s}}^{-1}$ towards north. Assuming the acceleration to be uniform, the change in velocity will be directed at

Forces of $1 \mathrm{N}, 2 \mathrm{N}$ and $3 \mathrm{N}$ act along the side $AB, BC, CA$ of an equilateral triangle $ABC$. Find their resultant.

A force of $60 \mathrm{N}$ acts on a body at an angle of $60°$ with the vertical. What are its rectangular components?

Two forces are acting at an angle of $120°$ to each other. The resultant of two forces is perpendicular to smaller forces. If greater force is $60 \mathrm{N}$, find the smaller force using triangle law of forces.

The angle between $A\text{ and }B\text{ is }\theta$. The value of the triple product $\overrightarrow{A}·\overrightarrow{B}\times \overrightarrow{A}$ isEnable GingerCannot connect to Ginger Check your internet connection
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The sum of the magnitudes of two forces inclined to each other at an angle in $8 \mathrm{N}$ and their resultant which is perpendicular to the smaller force is $4 \mathrm{N}$. Calculate the forces and angle between them.

The resultant of three vectors $1, 2\text{ and }3$ units whose directions are those of the sides of an equilateral triangle is at an angle of

What is the resultant of two forces $4 \mathrm{N}$ and $6 \mathrm{N}$ acting in directions inclined to each other at $60°$?

If $0.5 \hat{\mathrm{i}}+0.8 \hat{\mathrm{j}}+c \hat{\mathrm{k}}$ is a unit vector then $c$ is

The length of the sum of the vectors $\overrightarrow{a}=3 \hat{\mathrm{i}}$ and $\overrightarrow{b}=4 \hat{\mathrm{j}}$ is