Question

Five groups of four vectors are shown below. All magnitudes of individual vectors are equal. Please rank the groups based on the magnitude of the resultant vectors if the four vectors in each group were added together. Rank the groups of vectors from the greatest resultant magnitude to the smallest resultant magnitude.
Rank the groups of vectors from the greatest resultant magnitude to the smallest resultant magnitude.

Answer 1

With the addition of vectors we can find that the correct answer is:

   C)   Q> P > R =  S > T

The addition of vectors must be done taking into account that they have modulus and direction. The analytical method is one of the easiest methods, the method to do it is:

• Set a Cartesian coordinate system

• Decompose vectors into their components in a Cartesian system

• Perform the algebraic sums on each axis

• Find the resultant vector using the Pythagoras' Theorem to find the modulus and trigonometry to find the direction.

In this exercise indicate that the modulus of all vectors is the same, suppose that the value of the modulus is A.

We fix a Cartesian coordinate system with the horizontal x axis and the vertical y axis, we can see that we do not need to perform any decomposition, so we perform the algebraic sums

Diagram P

x-axis

         x = 2A

y-axis  

         y = 2A

The modulus of the resulting vector can be found with the Pythagorean Theorem

          P = $\sqrt{x^2+y^2}$

          P = $\sqrt{4A^2 +4A^2 }= \sqrt{8} \ A$

          P = 2 √2  A

         

Diagram Q

x-axis

        x = 3A

y-axis  

        y = A

Resulting

       Q = $\sqrt{x^2+y^2}$

       Q =$\sqrt{9A^2 + A^2 }$  

       Q = $\sqrt{10} \ A$

       

Diagram R

x- axis

       x = 0

y-axis

        y = 2 A

Resulting

       R =$\sqrt{4A^2 + 0}$  

       R = $\sqrt{4} \ A$

Diagram S

x-axis

       x = 2 A

y-axis

        y = 0

 

Resulting

       S = 2A

Diagram T

x- axis

      x = 0

y-axis  

      y = 0

Resultant T = 0

We order the diagram from highest to lowest

    Q> P> R = S> T

When reviewing the different answers, the correct one is:

   C.  Q> P> R = S> T

Learn more about adding vectors here:

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