Question

Vectors $\overrightarrow{A},\overrightarrow{B}$ and $\overrightarrow{C}$ have magnitudes $5,5\sqrt{2}$ and 5 respectively and direction of $\overrightarrow{A},\overrightarrow{B}$ and $\overrightarrow{C}$ are towards East, North - East and North respectively. If $\hat{i}$ and $\hat{j}$ are unit vectors along East and North respectively. The magnitude and direction of the resultant respectively will be

• A. $10\sqrt{2}$ towards north-east
• B. $10$ and ${45}^o$ from north-east
• C. $10$ and ${45}^o$ from north
• D. $10\sqrt{2}$ and ${45}^o$ from north-west

Answer 1

The correct option is A $10\sqrt{2}$ towards north-east

$\overrightarrow{A}=5\hat{i},\overrightarrow{C}=5\hat{j}$
$\overrightarrow{B}=5\sqrt{2}\cos 45\hat{i}+5\sqrt{2}\sin 45\hat{j}$
$=5\hat{i}+5\hat{j}$
$\overrightarrow{A}+\overrightarrow{B}+\overrightarrow{C}=5\hat{i}+5\hat{i}+5\hat{j}+5\hat{j}=10\hat{i}+10\hat{j}$
$|\overrightarrow{A}+\overrightarrow{B}+\overrightarrow{C}|=\sqrt{(10{)}^2+(10{)}^2}=10\sqrt{2}$
$\tan \theta =\frac{10}{10}=1$
$\theta ={45}^{\circ }$
Hence direction is North-East.