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Resultant Vector Calculator
Consider a person moving randomly like he is covering some distance in the east and some distance in the north. In such cases it is difficult to calculate the covered distance since direction is changing. Here we find Resultant.
Resultant vector is the vector obtained by adding the given vectors. If the two vector $\vec{x}$ and $\vec{y}$ are given. The Resultant Vector will be having the direction opposite to the given vectors.

Resultant Vector Calculator adds the given two vector values and gives the resultant of those.

Steps for Resultant Vector Calculator

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Step 1 :  

Read the problem. Given will the two vectors x and y.

Step 2 :  

The Resultant vector is given by the formula:
$\vec{R} = $\sqrt{\vec{x}^{2} + \vec{y}^{2}}$
Substituting these values in the above formula, we get the resultant vector.

Problems on Resultant Vector Calculator

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  1. A person starts driving his car from starting point to 50 miles east and then 40 miles north to reach his destiny. Draw and calculate the resultant vector from the beginning to the end of his journey.

    Step 1 :  

    given: $\vec{x}$ = 50 miles,

               $\vec{y}$ = 40 miles

    Step 2 :  

    The Resultant vector is given by: $\vec{R}$ = $\sqrt{\vec{x}^{2} + \vec{y}^{2}}$

    $\vec{R}^{2}$ = 502 + 402

    |R| = $\sqrt{4100}$

       = 64.03 miles.

    Answer  :  

     The Resultant vector of the distance travelled by the person is 64.03 miles.

  2. Rita walks 2 km to the east then 5 km to the south to reach her school. What is her displacement ? 

    Step 1 :  

    given: $\vec{x}$ = 2 km,

               $\vec{y}$ = 5 km

    Step 2 :  

    The Resultant vector is given by: $\vec{R}$ = $\sqrt{\vec{x}^{2} + \vec{y}^{2}}$

    R2 = 22 + 52

    |R| = $\sqrt{29}$

       = 5.385 km.

    Answer  :  

    The Resultant vector or displacement by rita is 5.385 km.

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