Question

Which equation represents the Pythagorean theorem, which can be used to find the magnitude of resultant vectors?


R = A + B

R = A x B

R2 = A2 x B2

R2 = A2 + B2

Answer 1

I will use capital letters to represent vectors.

To find a vector (magnitude + direction):

R  = A + B

To find only the direction of the vector:

theta = tan^-1(ycomponent/xcomponent)


To find the magnitude only ( your question)


R^2 = A^2 + B^2
R = sqrt( A^ 2 + B^2)  (last option: D)

Answer 2

The magnitude of the resulting vector can be calculated by Pythagorean theorem.

Given Here,

A and B are two vectors,

R - magnitude of resulting vector.

Vector:

Pythagorean theorem can be applied to calculate the magnitude of the vector because the line joining the tow vector form a triangle.

It is a unit that has both magnitude and direction.    

R  = A + B  

 

The magnitude of the resulting vector,  

$\bold {R^2 = A^2 + B^2}\\\\\bold {R = \sqrt( A^ 2 + B^2)}$

Therefore, the magnitude of the resulting vector can be calculated by Pythagorean theorem.

To know more about Vector quantity,

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