Resultant Vector Formula

Based on the direction of a vector to other vectors, the Resultant Vector formula is classified into three types.

Resultant Vector 1st Formula

If the vectors are in the same direction then the resultant of the vector can be calculated by adding the vectors which are in the same direction. Let “a” and “b” be the vectors with the same direction then the resultant vector “r” is given by

r = a + b

Resultant Vector 2nd formula

If the vectors are in different directions then the resultant of the vector can be calculated by subtracting the vectors from each other. Let “b” be a vector which is in the opposite direction to vector “a” then the resultant vector “r” is given by

r = a – b

Resultant Vector 3rd Formula

If any vectors are inclined to each other at some angle then the resultant of these vectors can be calculated by this formula. Let “a”, and “b” be two vectors inclined to each other at an angle θ, then the resultant vector “r” is given by:

R = A² + B² + 2ABcosΦ

where,

A², B² represents Square of Magnitude of Vector A, B

The image added below shows vector A and B and their resultant vector R.

Articles Related to Resultant Vector Formula:

• Scalar and Vector
• Dot and Cross Products on Vectors
• Vector Operations
• Triangle Law of Vector Addition

Resultant vector formula gives the resultant value of two or more vectors. The result is obtained by computing the vectors with consideration of the direction of each vector to others. This formula has various applications in Engineering & Physics.