Addition of Vectors

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. In a triangle $ABC,$ if $2\overrightarrow{AC}=3\overrightarrow{CB}$ and $2\overrightarrow{OA}+3\overrightarrow{OB}=\lambda \cdot \overrightarrow{OC},$ then $\lambda$ is

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. $None$
4. $\sqrt{5},\sqrt{12}$

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

1. $\overrightarrow{v}-\overrightarrow{b}$
2. $-\overrightarrow{b}$
3. $\overrightarrow{b}-2\overrightarrow{a}$
4. None of these

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

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

Q.

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

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

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

3. $4$, towards south

4. $4$, towards east

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

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

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.