Resultant of three Vectors

This article is about resultant of three vectors. Resultant of three vectors is vectors that results from adding two or more vectors together. There are two ways to calculate the resultant vector. There are many different websites to help the students on obtaining the resultant of three vectors. Tutor vista is the famous website to provide help on finding the resultant of three vectors with the help of highly qualified tutors. Below are some of the problems regarding resultant of three vectors.

Methods - Resultant of three Vectors:

There are two different methods to find the resultant vector.



The head to tail method:

The head to tail method is represented with the arrow mark. The arrow mark is the head and the tail is with out the arrow mark. Place the two vectors such that the head of the vectors joins the tail of another vector. Draw the resultant vector as shown in the figure above. To find the resultant vectors we use the Pythagorean theorem. There is also another method to calculate the resultant vector which is studied in college grade.

Parallelogram Method:

The another method is parallelogram method. To use this parallelogram method it is very important to be well know with trigonometry basics.


Example Problems - Resultant of three Vectors

vector addition is also the resultant of 3 vectors.

Example 1: The vector a = 3 and vector b = 4. Find the resultant vector using Pythagorean theorem.

Solution

We know that Pythagorean theorem is a2+b2 = c2

So given a =3 and b = 4

So the resultant vector c2 = a2 + b2

c =` sqrt (a^2 + b^2)`

= `sqrt (3^2 + 4^2)`

=` sqrt (9+16)`

= `sqrt(25)`

c = 5

So the resultant vector is 5


Example 2: Add 5`veci` +4`vecj`+3`veck` with 2`veci`+1`vecj`+0`veck`

Solution

Here two set of vectors are given. we have to perform the sum of two vectors by adding the magnitudes alone

5`veci` + 4`vecj` +3`veck`
2`veci` + 1`vecj` +0`veck`
----------------------
7`veci` + 5`vecj` + 3`veck`
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Example 3: `veca =4vecp + 3vecq+2vecr` , `vec b = 5vecp +2vecq+vecr` and `vecc = 2 vecp + vecq + 4 vecr`
Solution
Resultant vector is `veca + vecb + vecc`
`4 vecp + 3vecq+2 vecr`
`5 vecp + 2vecq+ vecr`
`2 vecp + vecq + 4 vecr`
---------------------------------
`11 vecp +6 vecq + 7 vecr`
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