Question

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

Answer 1

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

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=<v_x,v_y>`

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.

Answer 2

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