# First Year Physics Vectors and Equilibrium A load of 10 \mathrm{~N} is suspended from a clothes line. This distorts the line so that it makes an angle of 15^{\circ} with the horizontal at each end. Find the tension in the clothes line.

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##### A load of 10 \mathrm{~N} is suspended from a clothes line. This distorts the line so that it makes an angle of 15^{\circ} with the horizontal at each end. Find the tension in the clothes line.

A uniform beam of 200 \mathrm{~N} is supported horizontally as shown. If the breaking stress of the rope is 400 \mathrm{~N} how far can the man of weight 400 \mathrm{~N} walk from point A on the beam as shown in figure?

Show that the three vectors \hat{i}+\hat{j}+\hat{k} 2 \hat{i}-3 \hat{j}+\hat{k} and 4 \hat{i}+\hat{j}-5 \hat{k} are mutually perpendicular.

PROBLEM 2.18A uniform sphere of weight 10 \mathrm{~N} is held by a string attached to a frictionless wall so that the string makes an angle of 30^{\circ} with the wall. Find the tension in the string and the force exerted on the sphere by the wall.

Identify the correct answer:(ii) A horizontal force F is applied to a small object P of mass m at rest on a smooth plane inclined at an angle \theta to the horizontal as shown in figure. The magnitude of the resultant force acting up and along the surface of the plane on the object is:(a) F \cos \theta-\mathrm{mg} \sin \theta (b) \mathrm{F} \sin \theta-\mathrm{mg} \cos \theta (c) F \cos \theta+m g \cos \theta (d) F \sin \theta+m g \sin \theta (e) m g \tan \theta

Show that the sum and difference of two perpendicular vectors of equal lengths are also perpendicular and of the same length.

The magnitude of dot and cross products of two vectors are 6 \sqrt{3} and 6 respectively. Find the angle between the vector.

Vector \overrightarrow{\mathbf{A}} \overrightarrow{\mathbf{B}} and \overrightarrow{\mathbf{C}} are 4 unit north 3 unit west and 8 unit east respectively. Describe c arefully(c) \overrightarrow{\mathbf{B}} \times \overrightarrow{\mathbf{C}}

How would the two vectors of the same magnitude have to be oriented if they were to be combined to give a resultant equal to a vector of the same magnitude.

Two forces of magnitudes 10 \mathrm{~N} and 20 \mathrm{~N} act on a body in directions making angles 30^{\circ} and 60^{\circ} with x -axis respectively. Find the resultant force.

Suppose in a rectangular coordinates system a vector \vec{A} has its tail at the point P(-2-3) and its tip at Q(39) . Determine the distance between these two points?

Find the work done when the point of application of the force 3 \hat{\mathbf{i}}+2 \hat{\mathbf{j}} moves in a straight line from the point (2-1) to the point (64) .

Vector \overrightarrow{\mathbf{A}} \overrightarrow{\mathbf{B}} and \overrightarrow{\mathbf{C}} are 4 unit north 3 unit west and 8 unit east respectively. Describe c arefully (a) \overrightarrow{\mathbf{A}} \times \overrightarrow{\mathbf{B}}

Can the magnitude of a vector have a negative value?

Two particles are located at \overrightarrow{r_{1}}=3 \hat{i}+7 \hat{j} and \vec{r}_{2}=-2 \hat{i}+3 \hat{j} respectively. Find both the magnitude of vector \left(\overrightarrow{r_{2}}-\overrightarrow{r_{1}}\right) and its orientation with respect to the x -axis.

If \overrightarrow{\mathbf{A}}+\overrightarrow{\mathbf{B}}=\overrightarrow{0} what can you say about the components of the two vectors?

A force F=2 \hat{i}+3 \hat{j} units has its point of application moved from point A(13) to the point B(57) . Find the work done.

Vector A lies in the xy-plane. For what orientation will both of its rectangular components be negative. For what orientation will its components have opposite signs?

The vector sum of three vectors gives a zero resultant. What can be the orientation of the vectors?

Suppose in a rectangular coordinates system a vector \vec{A} has its tail at the point P(-2-3) and its tip at Q(39) . Determine the distance between these two points?

The two vectors to be combined have magnitudes 60 \mathrm{~N} and 35 \mathrm{~N} . Pick the correct answer from those given below and tell why is it the only one of the three that is correct.(i) 100 \mathrm{~N} (ii) \mathbf{7 0 N} (iii) 20 \mathrm{~N}

The line of action of a force \vec{F} passes through a point P of a body whose position vector in metre is \hat{i}-2 \hat{j}+\hat{k} . If \vec{F}=2 \hat{i}-3 \hat{j}+4 \hat{k} (in Newton) determine the torque about the point A whose position vector (in metre) is 2 \hat{i}+\hat{j}+\hat{k} .

If one of the rectangular components of a vector is not zero can its magnitude be zero? Explains.

Name the three different conditions that could make \overrightarrow{\mathbf{A}_{1}} \times \overrightarrow{\mathbf{A}_{2}}=0 .

Can a body rotate about its centre of gravity under the action of its weight?

The two vectors to be combined have magnitudes 60 \mathrm{~N} and 35 \mathrm{~N} . Pick the correct answer from those given below and tell why is it the only one of the three that is correct.(i) 100 \mathrm{~N} (ii) 70 \mathrm{~N} (iii) 20 \mathrm{~N}

A certain corner of a room is selected as the origin of the rectangular coordinate system. If an insect is crawling on an adjacent wall at a point having coordinates (21) where the units are in meters? What is the distance of the insect from this corner of the room?