Resultant vector is the vector sum got by adding two or more vectors. It will always be directed in the direction opposite to the given vectors and is denoted by R.

If the displacement vectors are x and y. The resultant vector is given by

Resultant vector Calculator finds the sum of two vectors and gives the resultant. Provided are the blocks where you are supposed to enter the given vectors to get its resultant vector.

## Resultant Vector Problems

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

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