**Steps to find the Resultant vector:**

Step 1 : Read the given problem and observe the given magnitude of the components x and y.

**Step 2 :** The Resultant vector formula is given by

R = $\sqrt{x^{2} + y^{2}}$

Put the values in the above formula to get the answer.

**Here are given solved problems on resultant vector which may be helpful for you.**

### Solved Examples

**Question 1: **A person takes a long way to reach the city. If he leaves the station and moves 20 km east and then 15 km north. Calculate the resultant vector for the given journey.

** Solution: **

Step 1 : The given vectors are $\vec{x}$ = 20 km,
$\vec{y}$ = 15 km

Step 2 : The Resultant vector is given by

R = $\sqrt{x^{2} + y^{2}}$

= $\sqrt{20^{2} + 15^{2}}$

= $\sqrt{625}$
= 25 km.

**Question 2: **A car travels 50 km/hr in the east then it covers 40 km/hr in the south. Calculate its resultant vector.

** Solution: **
Step 1: x = 50 km/hr in east direction,

y = 40 km/hr
in south direction

Step 2: The resultant vector is given by

R = $\sqrt{x^{2} + y^{2}}$

= $\sqrt{50^{2} + 40^{2}}$

= $\sqrt{4100}$
= 64.03 km/hr.

The resultant vector of the travel is 64.03 km/hr