Addition of Vectors

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. $\sqrt{3^2+4^2}N$
2. $\sqrt{3^2+4^2+3\times 4cos30}N$
3. $\sqrt{3^2+4^2+3\times 4\times sin30}N$
4. $\sqrt{3^2+4^2+2\times 3\times 4cos30}N$

Q. If $\overrightarrow{a},\overrightarrow{b},\overrightarrow{c},\overrightarrow{d}$ be the vectors represented by the sides of a quadrilateral, taken in order, then $\overrightarrow{a}+\overrightarrow{b}+\overrightarrow{c}+\overrightarrow{d}=0.$

1. False
2. True

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. 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. $3.6km,ta{n}^{-1}\left(\frac{2}{3}\right)$
2. $3.6km,ta{n}^{-1}\left(\frac{3}{2}\right)$
3. $Cannotbecalculated$
4. $3.6km,ta{n}^{-1}\left(\frac{5}{3}\right)$

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

Q. If the riverboat is crossing the river, with a velocity of 4 m/s along the north and the river is flowing with a velocity of 3 m/s along the west,


then what is the magnitude and direction of resultant velocity?

1. 5 m/s in south-east direction
2. 7 m/s in north-west direction
3. 5 m/s in north-west direction
4. 7 m/s in south-east direction

Q. If $\overrightarrow{a},\overrightarrow{b},\overrightarrow{c},\overrightarrow{d}$ be the vectors represented by the sides of a quadrilateral, taken in order, then $\overrightarrow{a}+\overrightarrow{b}+\overrightarrow{c}+\overrightarrow{d}=0.$

1. False
2. True

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. $3.6km,ta{n}^{-1}\left(\frac{2}{3}\right)$
2. $3.6km,ta{n}^{-1}\left(\frac{3}{2}\right)$
3. $Cannotbecalculated$
4. $3.6km,ta{n}^{-1}\left(\frac{5}{3}\right)$

Q. $ABCD$ is a parallelogram and $A_1$ and $B_1$ are the midpoints of sides $BC$ and $CD$, respectively. If $\overrightarrow{A{A}_1}+\overrightarrow{A{B}_1}=\lambda \overrightarrow{AC}$, then $\lambda$ is equal to

1. $\frac{1}{2}$
2. $1$
3. $\frac{3}{2}$
4. $2$

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. $\overrightarrow{0}$
2. $2\overrightarrow{AB}$
3. $3\overrightarrow{AB}$
4. $5\overrightarrow{AB}$

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. $\overrightarrow{0}$
2. $2\overrightarrow{AB}$
3. $3\overrightarrow{AB}$
4. $5\overrightarrow{AB}$

Q. If $\left(\overrightarrow{A}+\overrightarrow{B}\right|=\left(\overrightarrow{A}-\overrightarrow{B}\right|$ then it can be said that
vector A and vector B are
to each other.

1. perpendicular
2. parallel
3. $\mathrm{at}{45}^o\mathrm{to}\mathrm{each}\mathrm{other}$

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. $\overrightarrow{a}$

2. $2\overrightarrow{a}$

3. $3\overrightarrow{a}$

4. None of these

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. $(-\frac{2}{\sqrt{3}},\frac{1}{\sqrt{3}},-\frac{2}{\sqrt{3}})$