Resultant Vector Formula

The quantities that have both magnitude and direction are called vectors. If they are in the opposite direction or same direction, then we can add and subtract directly. But they are in the same direction, then we cannot add directly. For a case like this, we use the formula that will square root of the sum of squares of each vector.

The resultant vector formula is

\[\large \overrightarrow{R}=\sqrt{\overrightarrow{x^{2}}+\overrightarrow{y^{2}}}\]

Solved Example

Question: Calculate the resultant vector if

\(\begin{array}{l}\overrightarrow{x}=4\end{array} \)
\(\begin{array}{l}\overrightarrow{y}= 5\end{array} \)


From the formula we could say that

\(\begin{array}{l}\overrightarrow{R}=\sqrt{\overrightarrow{4^{2}}+\overrightarrow{5^{2}}}\end{array} \)

\(\begin{array}{l}\overrightarrow{R}=6.41\;cm\end{array} \)


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