Component of $3\hat{i}+4\hat{j}$ perpendicular to $\hat{i}+\hat{j}$ and in the same plane as that of $3\hat{i}+4\hat{j}$ is:

Given that $\overrightarrow{\mathrm{C} }= \overrightarrow{A } + \overrightarrow{B } \mathrm{and} \overrightarrow{\mathrm{C} }$ makes an angle $\mathrm{\alpha } \mathrm{with} \overrightarrow{\mathrm{A}} \mathrm{and} \mathrm{\beta } \mathrm{with} \overrightarrow{\mathrm{B}}$. Which of the following options is correct?

If the angle between the vector $\overrightarrow{A} and \overrightarrow{B}$ is  $\theta$, the value of the product $\left(\overrightarrow{B}\times \overrightarrow{A}\right).\overrightarrow{A}$ is equal to:

Assertion: The graph between P and Q is a straight line when P/Q is constant.
Reason: The straight-line graph means that P is proportional to Q or P is equal to a constant multiplied by Q.

Which one, of the following statements, is correct?

Two forces of magnitude F have a resultant of the same magnitude F. The angle between the two forces is 

Two forces with equal magnitudes F act on a body and the magnitude of the resultant force is F/3. The angle between the two forces is 

Two forces are such that the sum of their magnitudes is 18 N and their resultant is perpendicular to the smaller force and the magnitude of the resultant is 12 N. Then the magnitudes of the forces will be:

If two forces of 5 N each are acting along X and Y axes, then the magnitude and direction of resultant is 

If the magnitude of the sum of two vectors is equal to the magnitude of the difference of the two vectors, the angle between these vectors is:

 $$\begin{gathered} 1. 0^0 \\ 2. {90}^0 \\ 3. {45}^0 \\ 4. {180}^0 \end{gathered}$$

If the magnitude of the sum of two vectors is equal to the magnitude of the difference between the two vectors, the angle between these vectors is:

If vectors A = cosωt $\hat{i}$ + sinωt $\hat{j}$ and B = (cosωt/2) $\hat{i}$ + (sinωt/2) $\hat{j}$ are functions of time, then the value of t at which they are orthogonal to each other
 

Six vectors $\overrightarrow{a} through \overrightarrow{f}$ have the directions as indicated in the figure. Which of the following statements may be true?

A particle moves from a point $(-2\hat{\mathrm{i}}+5\hat{\mathrm{j}})$ to $(4\hat{\mathrm{j}}+3\hat{\mathrm{k}})$ when a force of $(4\hat{\mathrm{i}}+3\hat{\mathrm{j}}) N$ is applied. How much work has been done by the force?

In the given figure

Which of the sets given below may represent the magnitude of resultant of three vectors adding to zero?

A blind person after walking 10 steps in one direction, each of length 80 cm, turns randomly to the left or to the right by $90°.$ After walking a total of 40 steps the maximum possible displacement of the person from his starting position could be -

A truck travelling due north with 20m/s turns towards west and travels at the same speed. Then the change in velocity is -

What is the resultant of three coplanar forces: $300 \mathrm{N}$ at $0°$, $400 \mathrm{N}$ at $30°$ and $400 \mathrm{N}$ at $150°$?

Two forces, ${\mathrm{F}}_1$ and ${\mathrm{F}}_2$ are acting on a body. One force is doubled of the other force and the resultant is equal to the greater force. Then the angle between the two forces is -

If the angle between vector a and b is an acute angle, then the difference a$-$b is -

What displacement must be added to the displacement $25 \hat{\mathrm{i}}-6 \hat{\mathrm{j}} \mathrm{m}$  to give a displacement of $7.0 \mathrm{m}$ pointing in the x-direction?

A child pulls a box with a force of $200 \mathrm{N}$ at an angle of $60°$above the horizontal. Then the horizontaland vertical components of the force will be:
              

A man rows a boat at a speed of $18 \mathrm{km}/\mathrm{hr}$ in the northwest direction. The shoreline makes an angle of $15°$ south of west. The component of the velocity of the boat along the shoreline is:

A bird moves from point (1, -2) to (4, 2). If the speed of the bird is 10 m/sec, then the velocity vector of the bird is:

(A)  $5\left(\hat{\mathrm{i}}-2\hat{\mathrm{j}}\right)$

(B)  $5\left(4\hat{\mathrm{i}}+2\hat{\mathrm{j}}\right)$

(C)  $0.6\hat{\mathrm{i}}+0.8\hat{\mathrm{j}}$

(D)  $6\hat{\mathrm{i}}+8\hat{\mathrm{j}}$

If the angle between the unit vectors $\hat{\mathrm{a}}$ and $\hat{\mathrm{b}}$ is $60°$, then $|\hat{\mathrm{a}}-\hat{\mathrm{b}}|$ is :

For the figure -

Two constant forces ${\overrightarrow{\mathrm{F}}}_1=2\hat{\mathrm{i}}-3\hat{\mathrm{j}}+3\hat{\mathrm{k}} \left(\mathrm{N}\right)$ and ${\overrightarrow{\mathrm{F}}}_2=\hat{\mathrm{i}}+\hat{\mathrm{j}}-2\hat{\mathrm{k}} \left(\mathrm{N}\right)$ act on a body and displace it from the position ${\overrightarrow{\mathrm{r}}}_1=\hat{\mathrm{i}}+2\hat{\mathrm{j}}-2\hat{\mathrm{k}} \left(\mathrm{m}\right)$ to the position ${\overrightarrow{\mathrm{r}}}_2=7\hat{\mathrm{i}}+10\hat{\mathrm{j}}+5\hat{\mathrm{k}} \left(\mathrm{m}\right)$. What is the work done W? $[Given : W =\overrightarrow{F}.∆\overrightarrow{r}]$

A vector A points, vertically upward and, B points towards north. The vector product $\mathrm{A}\times \mathrm{B}$ is -

The linear velocity of a rotating body is given by $\overrightarrow{\mathrm{v}}=\overrightarrow{\mathrm{\omega }}\times \overrightarrow{\mathrm{r}}$, where $\mathrm{\omega }$ is the angular velocity and r is the radius vector. The angular velocity of a body, $\overrightarrow{\mathrm{\omega }}=\hat{\mathrm{i}}-2\hat{\mathrm{j}}+2\hat{\mathrm{k}}$ and their radius vector is  $\overrightarrow{\mathrm{r}}=4\hat{\mathrm{j}}-3\hat{\mathrm{k}}, \mathrm{then\; value\; of} \left|\overrightarrow{\mathrm{v}}\right|$ will be: