Question

If you know the components of a vector, what mathematical relationship can be used to find the magnitude of the vector?

Answer 1

If you know a vector’s vertical and horizontal components you have to only find  hypotenuse of a right triangle.

You can use the Pythagorean theorem (x2 + y2 = h2),

h=sqrt(x2+y2)

when  you know the horizontal and vertical components of a vector, you can use the tangent to find the angle because

tan(theta)=y/x

theta= inverse tangent y/x:

this will tell you direction

Answer 2

Answer:

The mathematical expression is $v=\sqrt{v_{x}^2+v_{y}^2}$        

Step-by-step explanation:

Given if we know the components of a vector, then we have to find what mathematical relationship can be used to find the magnitude of the vector.

In two-dimensional coordinate system, any vector can be broken into two components x and y -component.

$v=$

The vector v and its components horizontal and vertical components form a right angled triangle as shown in attachment below.

Using the Pythagoras Theorem in the right triangle

$v^2=v_{x}^2+v_{y}^2$

⇒ $v=\sqrt{v_{x}^2+v_{y}^2}$

The above mathematical relationship can be used to find the magnitude of the vector.