# Questions with detailed step by step solutions from Kinematics

##### Questions in Kinematics
1. The resultant of two vectors $\vec{A}$ and $\vec{B}$ is ${{\vec{R}}_{1}}.$ If the vector $\vec{B}$is reversed keeping $\vec{A}$ unchanged, the resultant becomes ${{\vec{R}}_{2}}.$ Which of the following is correct conclusion?
2. The resultant of two vectors $\vec{A}$ and $\vec{B}$ is ${{\vec{R}}_{1}}.$ If the vector $\vec{B}$ is reversed keeping $\vec{A}$ unchanged, the resultant becomes ${{\vec{R}}_{2}}.$ Which of the following is correct conclusion?
3. The sum of three vectors $\vec{A},\vec{B}$ and $\vec{C}$ is zero that is $\vec{A}+\vec{B}+\vec{C}=0$ and $A=B$ and $C=\sqrt{2}A.$ The angles between vectors $\vec{A}$and $\vec{B},\vec{B}$ and $\vec{C},\vec{C}$ and $\vec{A}$ are given by
4. The unit vector in the direction of $2\hat{i}-\hat{j}+3\hat{k}$ is
5. Three vectors are drawn from a point and they are $\vec{P}=3\hat{i}-4\hat{j}+5\hat{k}\,\,\,\,\vec{Q}=-3\hat{i}+4\hat{j}$ and $\vec{S}=-5\hat{k}.$ Their resultant is
6. The vertices of a quadrilateral are at $A(1,2,-1),\,\,B(-4,2,-2),\,\,C(4,1,-5)$ and $D(2,-1,3).$ Forces of magnitudes 2 N,3 N,2 N are acting at a point $A$ along the lines $AB,AC,AD$ of the quadrilateral respectively. Their resultant is (in N)
7. Given that $[\vec{P}=3\hat{i}+4\hat{j}.$ Which of the following is perpendicular to $\vec{P}$ ?
8. The position vectors of four points $A,B,C$ and $D$ are $\vec{a}=2\hat{i}+3\hat{j}+4\hat{k},\,\,\,\vec{b}=3\hat{i}+5\hat{j}+7\hat{k},\,\,\,\,$ $\vec{c}=\hat{i}+2\hat{j}+3\hat{k},\,\,\,\,\vec{d}=3\hat{i}+6\hat{j}+9\hat{k}$ respectively. Then vectors $\overrightarrow{AB}$ and $\overrightarrow{CD}$ are
9. What happens when we multiply a vector by $-2$ ?
10. A boy hangs from a horizontal bar by catching it in the two hands. Let the angle between the arms be $\theta$. For which of the following value of $\theta$, the tension in the arms will be largest?