Question

A person is moving towards east by a distance a unit and towards north by distance b then displacement vector is given as​

Answer 1

Explanation:

the answer is in the following figure

Answer 2

The magnitude of the resultant vector, |$\vec{r}$| = $\sqrt{a^{2}+b^{2}}$

Explanation:

Given data,

The displacement of a person towards east, AB = $\vec{a}$

The displacement of a person towards north, BC = $\vec{b}$

The resultant displacement vector is given by AC =  $\vec{r}$

The magnitude of the resultant vector,

                                    |$\vec{r}$| = $\sqrt{a^{2}+b^{2}}$

The direction of the resultant vector,

                      $\ahpha=tan^{-1}[\frac{bsin\theta}{a+bcos\theta}]$

Where θ  is the angle between two vectors, $\vec{a}$ and $\vec{b}$