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:

(1) $\frac{1}{2}(\hat{j}-\hat{i})$

(2) $\frac{3}{2}(\hat{j}-\hat{i})$

(3) $\frac{5}{2}(\hat{j}-\hat{i})$

(4) $\frac{7}{2}(\hat{j}-\hat{i})$

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

1.  $\mathrm{\alpha } \mathrm{cannot} \mathrm{be} \mathrm{less} \mathrm{then} \mathrm{\beta }$

2.  $\mathrm{\alpha } <\mathrm{\beta }, \mathrm{if} \mathrm{A}<\mathrm{B}$

3.  $\mathrm{\alpha } <\mathrm{\beta }, \mathrm{if} \mathrm{A}>\mathrm{B}$

4.  $\mathrm{\alpha } <\mathrm{\beta }, \mathrm{if} \mathrm{A}=\mathrm{B}$

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:

1. $B{A}^2 \cos \theta$

2. $B{A}^2 \sin \theta$

3. $B{A}^2 \sin \theta \cos \theta$

4. zero

Two forces A and B have a resultant $R_1$. If B is doubled, the new resultant $R_2$ is perpendicular to A. Then

(1) $R_1=A$

(2) $R_1=B$

(3) $R_2=A$

(4) $R_2=B$

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

1. 12 N, 6 N

2. 13 N, 5N

3. 10 N, 8 N

4. 16 N, 2 N

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

1. 90°

2. 45° 

3. 180° 

4. 0°

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

(a) $\overrightarrow{b}+\overrightarrow{c}=\overrightarrow{-f}$                        (b) $\overrightarrow{d}+\overrightarrow{c}=\overrightarrow{f}$

(c) $\overrightarrow{d}+\overrightarrow{e}=\overrightarrow{f}$                        (d) $\overrightarrow{b}+\overrightarrow{e}=\overrightarrow{f}$

In the given figure

(A)  Angle between $\overrightarrow{\mathrm{A}}$ and $\overrightarrow{\mathrm{B}}$ is $110°$

(B)  Angle between $\overrightarrow{\mathrm{C}}$ and $\overrightarrow{\mathrm{D}}$ is $60°$

(C)  Angle between $\overrightarrow{\mathrm{B}}$ and $\overrightarrow{\mathrm{C}}$ is $110°$

(D)  Angle between $\overrightarrow{\mathrm{B}}$ and $\overrightarrow{\mathrm{C}}$ is $70°$

A force of 6 N and another of 8 N can be applied together to produce the effect of a single force of -

(A)  1 N

(B)  11 N

(C)  15 N

(D)  20 N

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

(A)  2, 4, 8

(B)  4, 8, 16

(C)  1, 2, 1

(D)  0.5, 1, 2