Addition of vectors

Q. If a, b represent $\overrightarrow{AB},\overrightarrow{BC}$ respectively of a regular hexagon ABCDEF then $\overrightarrow{CD},\overrightarrow{DE},\overrightarrow{EF},\overrightarrow{FA}$ are

1. A-b, a, b, b-a
2. b-a, a, b, a-b
3. b-a, -a, -b, a-b
4. A-b, -a, -b, b-a

Q. Two soccer players kick a ball simultaneously from opposite sides. One kicks with 50N force towards east and other kicks with 30 N force towards west. What is the net force on the ball?

1. 30N towards west
2. 50N towards east
3. 20N
4. 20N towards east

Q.

The side of a regular hexagon is denoted by $h$. Express the perimeter in terms of $h$.

Q. Find the values of 'a' in each of the following :

Q. Let D, E, F be the middle points of the sides BC, CA, AB respectively of a $\Delta ABC$. Then, $\overrightarrow{AD}+\overrightarrow{BE}+\overrightarrow{CF}$ equals

1. $\overrightarrow{0}$
2. $2\overrightarrow{AB}$
3. $3\overrightarrow{AB}$
4. $Noneofthese$

Q. If ABCDEF is a regular hexagon with $\overrightarrow{AB}=\overrightarrow{a}$ and $\overrightarrow{BC}=\overrightarrow{b}$, then $\overrightarrow{CE}$

1. $Noneofthese$
2. $\overrightarrow{v}-\overrightarrow{b}$
3. $\overrightarrow{b}-2\overrightarrow{a}$
4. $-\overrightarrow{b}$

Q.

The vectors b and c are in the direction of north-east and north-west respectively and $|b|=|c|=4$. The magnitude and direction of the vector d = c - b, are

1. 4$\sqrt{2}$, towards north

2. 4$\sqrt{2}$, towards west

3. 4, towards east

4. 4, towards south

Q. Given the vectors $u=[-5,4]$ and $v=[3,-1],|2u-3v|=$

1. $[19,11]$
2. $\sqrt{482}$
3. $[19,13]$
4. $2\sqrt{41}-3\sqrt{10}$
5. $2\sqrt{65}$

Q.

$(\overrightarrow{a}.\hat{i})(\overrightarrow{a}\times \hat{i})+(\overrightarrow{a}.\hat{j})(\overrightarrow{a}\times \hat{j})+(\overrightarrow{a}.\hat{k})(\overrightarrow{a}\times \hat{k})$ is always equal to

1. None of these

2. $\overrightarrow{a}$

3. $3\overrightarrow{a}$

4. $2\overrightarrow{a}$

Q. $If\overrightarrow{a}=<3,-2,1>\overrightarrow{b}=<-1,1,1>$ then the unit vector parallel to the vector $\overrightarrow{a}+\overrightarrow{b}$ is

1. $<\frac{2}{3},-\frac{1}{3},\frac{2}{3}>$
2. $<\frac{2}{5},-\frac{1}{5},\frac{2}{5}>$
3. $<\frac{2}{\sqrt{3}},-\frac{1}{\sqrt{3}},\frac{2}{\sqrt{3}}>$
4. $<-\frac{2}{\sqrt{3}},\frac{1}{\sqrt{3}},-\frac{2}{\sqrt{3}}>$

Q. If the diagonals of a parallelogram are given $3\hat{i}+\hat{j}-2\hat{k}$ and $\hat{i}-3\hat{j}+4\hat{k}$, then the lengths of its sides are

1. $\sqrt{8},\sqrt{10}$
2. $\sqrt{6},\sqrt{14}$
3. $\sqrt{5},\sqrt{12}$
4. $None$

Q. AB, BC, CD, DE and EF are 5 vectors as shown in the figure.

Joining which 2 points will give the magnitude of resultant of $\overline{AB}+\overline{BC}+\overline{CD}+\overline{DE}+\overline{EF}$

1. A & F
2. A & D
3. A & C
4. A & E

Q. Two forces of 3N and 4N are acting on a particle. The forces are acting at an angle of ${30}^{\circ }$ between them. The magnitude of the resultant force will be

1. 
2. 
3. 
4. 

Q. A car goes 5 km east, 3km south, 2km west and 1km north. The magnitude of the resultant displacement will be ___ km at an angle of $ta{n}^{-1}$(- / -) with the positive x-axis (where x axis is in the east direction) in the clock wise direction.

1. 
2. 
3. 
4. None of hese

Q. The sides of a parallelogram are given by the vectors <2, 4, -5> and <1, 2, 3> , then the unit vector parallel to one of the
diagonals is

1. $\frac{1}{7}(3\hat{i}-6\hat{j}+2\hat{k})$
2. $\frac{1}{7}(3\hat{i}+6\hat{j}-2\hat{k})$
3. $\frac{1}{7}(-3\hat{i}+6\hat{j}-2\hat{k})$
4. $\frac{1}{7}(3\hat{i}+6\hat{j}+2\hat{k})$

Q. If the diagonals of a parallelogram are given $3\hat{i}+\hat{j}-2\hat{k}$ and $\hat{i}-3\hat{j}+4\hat{k}$, then the lengths of its sides are

1. $\sqrt{8},\sqrt{10}$
2. $\sqrt{6},\sqrt{14}$
3. $\sqrt{5},\sqrt{12}$
4. $None$

Q. $If\overrightarrow{a}=<3,-2,1>\overrightarrow{b}=<-1,1,1>$ then the unit vector parallel to the vector $\overrightarrow{a}+\overrightarrow{b}$ is

1. $<\frac{2}{5},-\frac{1}{5},\frac{2}{5}>$
2. $<\frac{2}{3},-\frac{1}{3},\frac{2}{3}>$
3. $<\frac{2}{\sqrt{3}},-\frac{1}{\sqrt{3}},\frac{2}{\sqrt{3}}>$
4. $<-\frac{2}{\sqrt{3}},\frac{1}{\sqrt{3}},-\frac{2}{\sqrt{3}}>$