Dot Product of Two Vectors

Q. If the vectors $\overrightarrow{a}=2\hat{i}+\lambda \hat{j}+\hat{k},\overrightarrow{b}=\hat{i}-2\hat{j}+3\hat{k}$ are perpendicular, then the value of $2\lambda$ is

Q.

$If\overrightarrow{A}=2\hat{i}-3\hat{j}\text{and}\overrightarrow{B}=-4\hat{i}+2\hat{j},\text{then}|\overrightarrow{A}.\overrightarrow{B}|=$ ___

Q.

$Themagnitudeoftheprojectionof2\hat{i}+3\hat{j}+4\hat{k}onthevector\hat{i}+\hat{j}+\hat{k}willbe\underset{–}{}$

1. 

2. 

3. 

4. None of the above

Q.

$Aforceof\overrightarrow{F}=3\hat{i}+4\hat{j}isactingonaboxatpoint\overrightarrow{A}whosepositionvectorwithrespecttooriginis<2,3>.Workdoneindisplacingtheparticlefrom\overrightarrow{A}to\overrightarrow{B}whosepositionvectorwithrespecttooriginis<5,6>willbe.......units$

__

Q.

George is pulling Cameron on a toboggan and is exerting a force of 40N acting at an angle of ${60}^{\circ }$ to the ground. If Cameron is pulled by a distance of 100 m horizontally, then the work done by George is __ J

Q.

The angle between the vectors $\overline{u}=<3,0>and\overline{v}=<5,5>$ is ___

Q.

If $\overline{a}and\overline{b}$ are two vectors as shown in the figure, then $\overline{a}.\overline{b}$ will equal to $|\overline{a}||\overline{b}|cos\theta$

1. True

2. False

Q.

$If\overline{a}.\overline{b}=\overline{a}.\overline{c}and\overline{a}\ne \overline{0},thenwecansaythat\overline{b}=\overline{c}.$

1. False

2. True

Q.

If $\overrightarrow{a}=x\hat{i}+(x-1)\hat{j}+\hat{k}$ and $\overrightarrow{b}=(x+1)\hat{i}+\hat{j}+a\hat{k}$ always make an acute angle with each other for every value of $xϵR$, then

1. $aϵ(-\infty ,2)$

2. $aϵ(2,\infty )$

3. $aϵ(-\infty ,1)$

4. $aϵ(1,\infty )$

Q.

Let P, Q, R and S be the points on the plane with position vectors
$-2\hat{i}-\hat{j},4\hat{i},3\hat{i}+3\hat{j}and-3\hat{i}+2\hat{j}$, respectively. The quadrilateral PQRS must be a

1. parallelogram, which is neither a rhombus nor a rectangle

2. square

3. rectangle, but not a square

4. rhombus, but not a square